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

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Answer 1 · 2018-06-10T12:19:50

#y=C_1xe^x#

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#