List of top Mathematics Questions on homogeneous differential equation

If \(x\frac{dy}{dx}=y(\log y-\log x+1)\) and its solution is \(y=[h(x)]e^{cx}\), then \(h(x)=\ldots\)
If the general solution of the differential equation \(y\sec ^{2}\left(\frac{x}{y}\right)dx-\left(x\sec ^{2}\left(\frac{x}{y}\right)-y\right)dy=0\) is \(\tan \left(\frac{x}{y}\right)+g(y)=c\), then \(g(y)=\ldots\)
The solution of the differential equation \(y^{2}-x^{2}\frac{dy}{dx}=xy\frac{dy}{dx}\) is ...
The general solution of the differential equation \[ y(2x+y)\,dx=x(x+y)\,dy \] is
For the differential equation \((x^2+y^2)\,dy = xy\,dx\), it is given that \(y(1) = 1\) and \(y(x_0) = e\), then the value of \(x_0\) is _____
The equation of the curve passing through the point (0, 1) and having a slope of the tangent at point \(P(x,y)\) is equal to \(\frac{y}{x+y}\), is
The solution of the differential equation \(\frac{dy}{dx} = \frac{x+y}{x-y}\) is
The differential equation is \[ \frac{dy}{dx}+\frac{y}{x}=0 \] and \(y(1)=2\). Then the value of \(y(3)\) is

If \(x \frac{\mathrm{~d} y}{\mathrm{~d} x}=y(\log y-\log x+1)\), then the solution of the equation is

Which of the following is not a homogeneous function?

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

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

If \[ \cos\frac{y}{x}=A\log x+C \] is the general solution of \[ \left(x\sin\frac{y}{x}\right)dy=\left(y\sin\frac{y}{x}-x\right)dx, \] then \(A=\)
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