Question

Solve the differential equation dy/dx=2*y/x,x>0 simplify?

Answer 1

Separate your variables:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2y}x\implies \dfrac{\mathrm dy}y=2\dfrac{\mathrm dx}x$

Integrating both sides gives

$\displaystyle\int\frac{\mathrm dy}y=2\int\frac{\mathrm dx}x\implies \ln|y|=2\ln|x|+C\implies y=e^{2\ln|x|+C}=Cx^2$