Find the general solution of xdy/dx = xy + y ?
1 Answer
Jun 10, 2018
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=e^(x+ln(x)+C)
Simplify
y=C_1xe^x