List of top Mathematics Questions on homogeneous differential equation

The differential equation is \[ \frac{dy}{dx}+\frac{y}{x}=0 \] and \(y(1)=2\). Then the value of \(y(3)\) is

The solution of the differential equation $\frac{dy}{dx} = \frac{x+y}{x-y}$ is

The general solution of differential equation $(y^2 - x^2)dx = xy dy$ ($x \neq 0$) is ______.

Solution of the differential equation $y' = \frac{x^2+y^2}{xy}$, where $y(1) = -2$ is given by

The general solution of $\frac{dy}{dx} = \frac{x+y}{x-y}$ is

The general solution of the differential equation. \[ \left( \frac{y}{x} \right) \cos \left( \frac{y}{x} \right) dx - \left[ \left( \frac{x}{y} \right) \sin \left( \frac{y}{x} \right) + \cos \left( \frac{y}{x} \right) \right] dy = 0 \] is

The general solution of $\left(x \frac{dy}{dx} - y\right) \sin \frac{y}{x} = x^3 e^x$ is

The general solution of the differential equation $(3xy + y^2)dx + (x^2 + xy)dy = 0$ is

The solution of the differential equation $\frac{x \frac{dy}{dx} - y}{\sqrt{x^2 - y^2}} = 10x^2$ is:

The real value of \( m \) for which the substitution \( y = u^m \) will transform the differential equation \( 2x^4 y \frac{dy}{dx} + y^4 = 4x^6 \) into a homogeneous equation is