List of top Mathematics Questions on Differential Equations asked in UP Board XII

Find the general solution of differential equation \( ydx + (x - y^2)dy = 0 \).
Find the degree of the differential equation \[xy \frac{d^2y}{dx^2} + x \left( \frac{dy}{dx} \right)^2 - y \left( \frac{dy}{dx} \right) = 2\]
The degree of differential equation \[ 9 \frac{d^2y}{dx^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{\frac{1}{3}} \text{ is} \]
The degree of differential equation \[ 9 \frac{d^2y}{dx^2} = \left\{ 1 + \left(\frac{dy}{dx}\right)^2 \right\}^{\tfrac{3}{2}} \] is
If \( y = e^{\tan^{-1}x} \), prove that \( (1 + x^2)\frac{d^2y}{dx^2} + (2x - 1)\frac{dy}{dx} = 0 \).
Obtain the differential equation of the family of curves \(y = \frac{2ce^{2x}}{1+ce^{2x}}\).
Solve: \((\tan^{-1}y - x)dy = (1+y^2)dx\).
Find a particular solution of the differential equation \( (x - y) (dx + dy) = dx - dy \) when \( y = -1 \) if \( x = 0 \).
Find the general solution of differential equation \( ydx + (x - y^2)dy = 0 \).
If \( y = \sin^{-1} x \), then prove that \( (1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} = 0 \).
Solve: \( (1 + x^2)\frac{dy}{dx} + 2xy - 4x^2 = 0 \).
If \(y = \cos^{-1} x\), then show that \((1 - x^2)\frac{d^2y}{dx^2} - x\frac{dy}{dx} = 0\).
The degree of the differential equation \(7\left(\frac{d^3y}{dx^3}\right)^2 + 5\left(\frac{d^2y}{dx^2}\right)^3 + x\frac{dy}{dx} + y = 0\) will be
Solve: \(\frac{dy}{dx} = \frac{x+y+1}{2x+2y+3}\).
Solve: \((1+y^2) dx = (\tan^{-1} y - x) dy\).
Find the differential equation representing the family of curves \(y=2mx\).
The number of arbitrary constants in a general solution of a differential equation of fifth order is
Solve : \( \frac{dy}{dx} = \frac{x + 2y - 3}{2x + y - 3} \).
Find the differential equation of the family of curves denoted by \(y = a \sin(x+b)\), where a and b are arbitrary constants.
If y = 5x\(^2\) + 4, then at the point with x-coordinate 2, the slope is
Find the general solution of the differential equation \(y - x \frac{dy}{dx} = x + y \frac{dy}{dx}\).
Find the general solution of the differential equation \(x\frac{dy}{dx} + 2y = x^2\) (\(x \neq 0\)).
The order of the differential equation \( \left( \frac{d^3y}{dx^3} \right)^2 + \log x \left( \frac{d^2y}{dx^2} \right)^3 + 5y = \cos x \) will be
Solve: \(ydx - (x + 2y^2)dy = 0\).
For the differential equation \(xy\frac{dy}{dx} = (x+2)(y+2)\), find the curve passing through the point \((1, -1)\).