Differential Equations - Calculus - Mathematics Previous Year Questions

The general solution of the linear differential equation \(\frac{d y}{d x}+\sec x \cdot y=\tan x\left(0 \leq x \leq \frac{\pi}{2}\right)\) is

The particular solution of the differential equation \(\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x\), such that \(y(\pi / 2)=0\) is

On solving the differential equation \(x^2 y d x-\left(x^3+y^3\right) d y=0\), the value of \(\log y\) is

Find the solution of equation \(\frac{d y}{d x}=\frac{1}{\cos (x+y)}\)

Find the solution of \(\frac{d y}{d x}=\frac{1}{\cos (x-y)}\)

The solution of the equation \(\frac{d y}{d x}+x(x+y)=x^3(x+y)^3-1\) is

The solution of \(\frac{d y}{d x}=1+x+y+x y\) is

If \(p\) and \(q\) are order and degree of the question \(\left(\frac{d^2 y}{d x^2}\right)^4+4 \frac{\left(\frac{d^2 y}{d x^2}\right)^2}{\left(\frac{d^3 y}{d x^3}\right)^3}+\frac{d^3 y}{d x^3}=x^2-1\), then

The solution of \(d y / d x=1+x+y+x y\) is

The solution of differential equation \(y y^{\prime}=x\left(\frac{y^2}{x^2}+\frac{f\left(y^2 / x^2\right)}{f^{\prime}\left(y^2 / x^2\right)}\right)\) is

If \(m\) and \(n\) are order and degree of the question \(\left(\frac{d^2 y}{d x^2}\right)^4+8 \frac{\left(d^2 y / d x^2\right)^3}{\left(d^4 y / d x^4\right)^5}+\left(\frac{d^4 y}{d x^4}\right)=x^2+4\), then \(m-n\) is equal to

If \(x d y / d x=x^2+y-2, y(1)=1\), then \(y(2)\) is equal to

The differential equation corresponding to the family of curves $y=e^x(a x+b)$ is