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Previous year question hub

Differential Equations - Calculus - Mathematics Previous Year Questions

Practice Differential Equations - Calculus - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

14Papers
3Years
42Questions
1Topics

Differential Equations question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Differential Equations. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 42 100%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 42 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
42 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
42 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Differential Equations
42 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT
3 Qs
TS EAMCET 2023 ONLINE 13TH MAY MORNING SHIFT
3 Qs
TS EAMCET 2023 ONLINE 14TH MAY EVENING SHIFT
3 Qs
TS EAMCET 2023 ONLINE 14TH MAY MORNING SHIFT
3 Qs
TS EAMCET 2023 (Online) 12th May Morning Shift
2 Qs
TS EAMCET 2023 ONLINE 13TH MAY EVENING SHIFT
2 Qs
TS EAMCET 2022 (Online) 19th July Evening Shift
3 Qs
TS EAMCET 2022 (Online) 19th July Morning Shift
3 Qs
TS EAMCET 2022 (Online) 20th July Evening Shift
3 Qs
TS EAMCET 2022 (Online) 20th July Morning Shift
3 Qs
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT
3 Qs
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT
3 Qs
TS EAMCET 2020 (Online) 10th September Evening Shift
5 Qs
TS EAMCET 2020 (Online) 10th September Morning Shift
3 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
TS EAMCET 2023 (Online) 12th May Morning Shift20232View paper
TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT20233View paper
TS EAMCET 2023 ONLINE 13TH MAY EVENING SHIFT20232View paper
TS EAMCET 2023 ONLINE 13TH MAY MORNING SHIFT20233View paper
TS EAMCET 2023 ONLINE 14TH MAY EVENING SHIFT20233View paper
TS EAMCET 2023 ONLINE 14TH MAY MORNING SHIFT20233View paper
TS EAMCET 2022 (Online) 19th July Evening Shift20223View paper
TS EAMCET 2022 (Online) 19th July Morning Shift20223View paper
TS EAMCET 2022 (Online) 20th July Evening Shift20223View paper
TS EAMCET 2022 (Online) 20th July Morning Shift20223View paper
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT20223View paper
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT20223View paper
TS EAMCET 2020 (Online) 10th September Evening Shift20205View paper
TS EAMCET 2020 (Online) 10th September Morning Shift20203View paper

All Differential Equations previous year questions

Practice every matching question in batches of 20, with every available option.

1
2022 · Mathematics · Calculus · Differential Equations
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT

The differential equation corresponding to the family of curves given by $a x^2+b y^2=1$, where $a$ and $b$ are arbitrary constants is

A

$x \frac{d^2 y}{d x^2}=\frac{d y}{d x}$

B

$x y \frac{d^2 y}{d x^2}+x\left(\frac{d y}{d x}\right)^2-y \frac{d y}{d x}=0$

C

$x y \frac{d^2 y}{d x^2}+y\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=0$

D

$x y \frac{d^2 y}{d x^2}-x\left(\frac{d y}{d x}\right)^2+y \frac{d y}{d x}=0$

Open complete paper
2
2022 · Mathematics · Calculus · Differential Equations
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT

For the differential equation

$$\sqrt{\frac{d^2 y}{d x^2}}=\sqrt[3]{\left[y \frac{d y}{d x}+x \sin \left(\frac{d y}{d x}\right)\right]^2}$$

A

Order is 2 and degree is 3

B

Order is 3 and degree is 3

C

Order is 3 and degree is 2

D

Order is 2 and degree is not defined

Open complete paper
3
2022 · Mathematics · Calculus · Differential Equations
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT

The general solution of the differential equation $\frac{d y}{d x}=\frac{x y+x-2 y-2}{x y-2 x+y-2}$ is

A

$x+y+3 \log \left|\frac{x+1}{y+1}\right|=c$

B

$x+y+3 \log \left|\frac{y+1}{x+1}\right|=c$

C

$x-y+3 \log \left|\frac{x+1}{y+1}\right|=c$

D

$x-y+3 \log \left|\frac{y+1}{x+1}\right|=c$

Open complete paper
4
2022 · Mathematics · Calculus · Differential Equations
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT

The curve that satisfies the differential equation $x y d y-\left(1+y^2\right) d x=0$ passes through $(1,0)$ and intersects the curve $x^2+3 y^2=3$ at an angle $\theta$. Then, $\frac{2 \theta}{\pi}=$

A

2

B

0

C

4

D

1

Open complete paper
5
2022 · Mathematics · Calculus · Differential Equations
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT

The differential equation of the family of circles with fixed radius $r$ units and centre on the line $y=3$, is

A

$1+\left(\frac{d y}{d x}\right)^2=\frac{r^2}{(y-3)^2}$

B

$1+\left(\frac{d y}{d x}\right)^2=\frac{r^2}{y-3}$

C

$\left(\frac{d y}{d x}\right)^2=\frac{r^2}{(y-3)^2}$

D

$\left(\frac{d y}{d x}\right)^2=\frac{r^2}{y-3}$

Open complete paper
6
2022 · Mathematics · Calculus · Differential Equations
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT

The degree of the differential equation

$$x\left(\frac{d^2 y}{d x^2}\right)^{1 / 3}+2 x^2\left(\frac{d^2 y}{d x^2}\right)^{5 / 3}+7 \frac{d y}{d x}+y=0$$

A

15

B

5

C

12

D

3

Open complete paper
7
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT

The degree and order of the differential equation of the family of parabolas whose axis is the $X$-axis, are respectively

A
2,2
B
2,1
C
$1,2^{\circ}$
D
3,2
Open complete paper
8
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT
The general solution of the differential equation $\left(2 x-10 y^3\right) d y+y d x=0, y \neq 0$ is
A
$x^2 y-2 y^3=C$
B
$x y^2-2 y^5=C$
C
$x y^3+2 y=C$
D
$x y^2+3 y=C$
Open complete paper
9
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT

The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x$ is

A
$\sin ^{-1}\left(\frac{y}{x}\right)=\frac{x}{2}+C$
B
$\sin \left(\frac{x}{y}\right)=\frac{x^2}{2}+C$
C
$\sin \left(\frac{y}{x}\right)=\log |x|+C$
D
$\cos \left(\frac{y}{x}\right)=\log |x|+C$
Open complete paper
10
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 13TH MAY EVENING SHIFT

The general solution of the differential equation $(\sec x+\tan x) \frac{d y}{d x}+\left(\sec ^2 x+\sec x \tan x\right) y=1$ is

A

$(1+\sin x) y=n \cos x+C$

B

$(1+\cos x) y=x \sin x+C$

C

$(\sec x+\tan x) y=x \sec x+C$

D

$(\sec x+\tan x) y=x+C$

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11
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 13TH MAY EVENING SHIFT

The general solution of the differential equation $(3 x-4 y)(d x-3 d y)+(6 d x-4 d y)=0$ is

A

$x-2 y+\log |3 x-4 y+6|=C$

B

$5 x-15 y-4 \log |15 x-20 y-12|=C$

C

$5 x-15 y+14 \log |15 x-20 y-12|=C$

D

$8 y-4 x+\log |9 x-12 y+4|=C$

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12
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 13TH MAY MORNING SHIFT

The general solution of the differential equation $\frac{d y}{d x}=\sin (x-y)+\cos (x-y)$ is

A

$\log \left|\frac{\tan \frac{(x-y)}{2}+1}{\tan \frac{(x-y)}{2}}\right|=x+C$

B

$\log \left|\frac{\tan \frac{(x-y)}{2}-1}{\tan \frac{(x-y)}{2}}\right|=x+C$

C

$\log \left|\frac{\tan (x-y)-1}{\tan (x-y)}\right|=x+C$

D

$\log \left|\frac{\sin (x-y)+\cos (x-y)}{\cos (x-y)}\right|=x+C$

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13
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 13TH MAY MORNING SHIFT

The general solution of the differential equation $x^2 d y-\left(x y-y^2\right) d x=0$ is

A

$y^2=3 x^2 \log (C x)$

B

$y^2=\log x+C$

C

$y \log x=x+C y$

D

$y \log x=x^2+C$

Open complete paper
14
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 13TH MAY MORNING SHIFT

If $A$ and $B$ are arbitrary constants, then the differential equation having $y=A e^x+B \sin 2 x$ as its general solution is

A

\(\begin{aligned} & (\cos 2 x-\sin 2 x) \frac{d^2 y}{d x^2}+(4 \sin 2 x) \frac{d y}{d x} -4(\sin 2 x+\cos 2 x) y=0 \end{aligned}\)

B

\(\begin{aligned} & (\cos 2 x+\sin 2 x) \frac{d^2 y}{d x^2}+(4 \sin 2 x) \frac{d y}{d x} -4(\sin 2 x-\cos 2 x) y=0 \end{aligned}\)

C

\(\begin{aligned} & (\cos 2 x-\sin 2 x) \frac{d^2 y}{d x^2}+(4 \sin 2 x) \frac{d y}{d x} +4(\sin 2 x+\cos 2 x) y=0 \end{aligned}\)

D

\(\begin{aligned} & (\sin 2 x-\cos 2 x) \frac{d^2 y}{d x^2}-(4 \sin 2 x) \frac{d y}{d x} -4(\sin 2 x+\cos 2 x) y=0 \end{aligned}\)

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15
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 14TH MAY EVENING SHIFT

If the solution for the differential equation $y^2 d x+\left(x^2-x y-y^2\right) d y=0$ at $(2,1)$ is $x+y=k\left(x y^2-y^3\right)$, then $k=$

A

-3

B

-4

C

4

D

3

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16
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 14TH MAY EVENING SHIFT

The general solution of the differential equation $\frac{d y}{d x}+\frac{y}{x}=x^2$ is

A

$x y=\frac{x^2}{2}+C$

B

$x y=\frac{x^3}{3}+C$

C

$x y=\frac{x^4}{4}+C$

D

$x y=\frac{x^5}{5}+C$

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17
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 14TH MAY EVENING SHIFT

If $a$ and $b$ are the arbitrary constants, then the differential equation corresponding to the family of curves given by $y=x[a \cos (\log x)+b \sin (\log x)]$ is

A

$x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-2 y=0$

B

$x^2 \frac{d^2 y}{d x^2}-x \frac{d y}{d x}+2 y=0$

C

$x^2 \frac{d^2 y}{d x^2}-x \frac{d y}{d x}-2 y=0$

D

$x^2 \frac{d^2 y}{d x^2}-x \frac{d y}{d x}+y=0$

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18
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 14TH MAY MORNING SHIFT

If the solution of the differential equation $\frac{d y}{d x}=\frac{2 x+3 y}{3 x-2 y}$ is $y=x \tan (f(x))+C$, then $f(x)=$

A

$\frac{1}{3} \log \left(x^2+y^2\right)$

B

$(2 x+3 y) \log x$

C

$x \log \frac{y}{x}+y^2$

D

$\sin \left(x+y^2\right)$

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19
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 14TH MAY MORNING SHIFT

The general solution of the differential equation $\left(x^2+2\right) d y+2 x y d x=e^x\left(x^2+2\right) d x$ is

A

$\frac{x}{y}=e^x\left(x^2+x-4\right)+C$

B

$2 x y=e^x\left(x^2-2 x+4\right)+C$

C

$\left(x^2+2\right) y=e^x\left(x^2-2 x+4\right)+C$

D

$\left(x^2+2\right)^2 y=e^x\left(x^2+2 x-4\right)+C$

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20
2023 · Mathematics · Calculus · Differential Equations
TS EAMCET 2023 ONLINE 14TH MAY MORNING SHIFT

If the order and degree of the differential equation corresponding to the family of curves $y^2=4 a(x+a)(a$ is parameter) are $m$ and $n$ respectively, then $m+n^2=$

A

3

B

4

C

5

D

2

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Showing 20 of 42 questions