Question

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

Answer 1

Separate your variables:


`(\mathrm dy)/(\mathrm dx)=\frac{2y}x\implies \frac{\mathrm dy}y=2\frac{\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`