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

For \( 0 < a < 1 \), the value of the integral \[ \int_{0}^{\frac{\pi}{2}} \frac{dx}{1 - 2a \cos x + a^2} \] 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