What is the solution for (dy)/(dx)-y/x =2xe^x,y(1)=2e-8 ?

The solution for (dy)/(dx)-y/x =2xe^x,y(1)=2e-8 is y=2e^xx-8x

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(dy)/(dx)-y/x =2xe^x,y(1)=2e-8

\frac{d y}{d x} - \frac{y}{x} = 2 x e^{x}, y (1) = 2 e - 8

y = 2 e^{x} x - 8 x

Solution steps

\frac{d y}{d x} - \frac{y}{x} = 2 x e^{x}

Solve linear ODE:

y = 2 e^{x} x - 8 x

y = 2 e^{x} x - 8 x

\int (sec^{2} (θ) + sec (θ) tan (θ)) d θ

\frac{d}{d y} (x y)

\frac{\partial}{\partial y} (2 - y - 2 x)

\frac{\partial}{\partial x} (x^{2} y sin (\frac{1}{x}))

What is the solution for (dy)/(dx)-y/x =2xe^x,y(1)=2e-8 ?
The solution for (dy)/(dx)-y/x =2xe^x,y(1)=2e-8 is y=2e^xx-8x