What is the solution for x(dy)/(dx)+2y=2e^x ?

The solution for x(dy)/(dx)+2y=2e^x is y=(2(e^xx-e^x))/(x^2)+(c_{1})/(x^2)

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x(dy)/(dx)+2y=2e^x

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

y = \frac{2 ( e ^{x} x - e ^{x} )}{x ^{2}} + \frac{c _{1}}{x ^{2}}

Solution steps

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

Solve linear ODE:

y = \frac{2 ( e ^{x} x - e ^{x} )}{x ^{2}} + \frac{c _{1}}{x ^{2}}

y = \frac{2 ( e ^{x} x - e ^{x} )}{x ^{2}} + \frac{c _{1}}{x ^{2}}

What is the solution for x(dy)/(dx)+2y=2e^x ?
The solution for x(dy)/(dx)+2y=2e^x is y=(2(e^xx-e^x))/(x^2)+(c_{1})/(x^2)