The general solution of the differential equation $\left(y^2-x^3\right) d x-x y d y=0(x \neq 0)$ is : (where c is a constant of integration)

Let $y=y(x)$ be the solution of the differential equation, $x \frac{d y}{d x}+y=x \log _e x x,(x>1)$. If $2 y(2)=\log _e 4-1$, then $y(e)$ is...

Let $y=y(x)$ be the solution of the differential equation, $\frac{2+\sin x}{y+1} \cdot \frac{d y}{d x}-\cos x, y>0, y(0)=1$. If $y(\pi) =a$ and $\frac{d y}{d x}$...

If for $x \geq 0, y=y(x)$ is the solution of the differential equation, $(x+1) d y=\left((x+1)^2+y-3\right) d x, y(2)=0$, then $\mathrm{y}(3)$ is equal to $\_\_\_\_$...

Let $f:[0,1] \rightarrow R$ be such that $f(x y)=f(x) \cdot f(y)$, for all $x, y \in[0,1]$, and $f(0) \neq 0$. If $y=y(x)$ satisfies the differential...

If $y=y(x)$ is the solution of the differential equation $\frac{5+\mathrm{e}^{\mathrm{x}}}{2+\mathrm{y}} \cdot \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{e}^{\mathrm{x}}=0$ satisfying $\mathrm{y}(0)=1$, then a value of $y\left(\log _e 13\right)$ is :

The general solution of the differential equation $\sqrt{1+x^2+y^2+x^2 y^2}+x y \frac{d y}{d x}=0$ is : (where C is a constant of integration)