Find the general solution of xdy/dx = xy + y ?

1 Answer
Jun 10, 2018

y=C_1xe^x

Explanation:

We want to solve the differential equation

xdy/dx=xy+y

This can solved by separation of variables

Separate the variables

xdy/dx=y(x+1)

=>1/ydy=(x+1)/xdx

Integrate both sides

int1/ydy=int(x+1)/xdx

=>ln(y)=x+ln(x)+C

Solve for y

y=e^(x+ln(x)+C)

Simplify

y=C_1xe^x