Differential Equations - Calculus - Mathematics Previous Year Questions

The order and degree of the differential equation \({\left[ {1 + {{\left( {{{dy} \over {dx}}} \right)}^5}} \right]^{{1 \over 3}}} = {{{d^2}y} \over {d{x^2}}}\) are respectively

The differential equation of the family of straight lines whose slope is equal to y-intercept is

The solution of the differential equation \(y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^2}} \over {{x^2}}}} \right)} \over {\phi '\left( {{{{y^2}} \over {{x^2}}}} \right)}}} \right]\) is (where, C is a constant)

The solution of the differential equation \((1 + {y^2}) + (x - {e^{{{\tan }^{ - 1}}y}}){{dy} \over {dx}} = 0\) is

The solution of the differential equation \({\sec ^2}x\tan ydx + {\sec ^2}y\tan xdy = 0\) is

The solution of the differential equation \({{{d^2}y} \over {d{x^2}}} = 0\) represents

The solution of the differential equation \(x \frac{d y}{d x}=\cot y\) is

The solution of the differential equation \(\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0\) is

The particular solution of \(e^{\frac{d y}{d x}}=2 x+1\) given that \(y=1\) when \(x=0\) is

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

The sum of the degree and order of the following differential equation \(\left[1-\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}=k x \frac{d^2 y}{d x^2}\)

The solution of the differential equation \(\frac{d y}{d x}+y \cos x=\frac{1}{2} \sin 2 x\)

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

$$\text { The general solution of } \frac{d y}{d x}=\sin ^{-1} x \text { is }$$

$$\text { Integrating factor of the differential equation } \frac{d y}{d x}+y=\frac{x^3+y}{x} \text { is }$$

Degree of the differential equation \(\log \left(\frac{d y}{d x}\right)^{\frac{1}{2}}=5 x+4 y\) is

The sum of the order and degree of the differential equation \(\left(\frac{d^2 y}{d x^2}\right)^5+\frac{4\left(\frac{d^2 y}{d x^2}\right)^3}{\left(\frac{d^3 y}{d x^3}\right)}+\frac{d^3 y}{d x^3}=x^2-1\) is

$$\text { If } \frac{d y}{d x}=y+3>0 \text { and } y(0)=2 \text { then } y(\log 2) \text { is equal to }$$

$$\text { The general solution of the differential equation }(1+\tan y)(d x-d y)+2 x d y=0 \text { is }$$

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