The solution for the differential equation $\frac{dy}{y} + \frac{dx}{x} = 0$ is:

Find the general solution of the differential equation: $\frac{dy}{dx} = (1+x^2)(1+y^2)$

Given that the slope of the tangent to a curve $y=y(x)$ at any point $(x, y)$ is $\frac{2y}{x^2}$. If the curve passes through the centre of the circle $x^2+y^2-2x-2y=0$,then its equation is

Let $f: R \rightarrow R$ be a differentiable function with $f(0)=0$. If $y=f(x)$ satisfies the differential equation $\frac{dy}{dx}=(2+5y)(5y-2)$,then the value of $\lim_{x \rightarrow -\infty} f(x)$ is:

The solution of $\log \left( \frac{dy}{dx} \right) = ax + by$ is

The general solution of the differential equation $\frac{dy}{dx} = \frac{x+y+1}{x+y-1}$ is given by