What is the solution for x(dy)/(dx)+2y=-3e^x ?

The solution for x(dy)/(dx)+2y=-3e^x is y=-(3(e^xx-e^x))/(x^2)+(c_{1})/(x^2)

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x(dy)/(dx)+2y=-3e^x

x \frac{d y}{d x} + 2 y = - 3 e^{x}

y = - \frac{3 ( e ^{x} x - e ^{x} )}{x ^{2}} + \frac{c _{1}}{x ^{2}}

Solution steps

x \frac{d y}{d x} + 2 y = - 3 e^{x}

Solve linear ODE:

y = - \frac{3 ( e ^{x} x - e ^{x} )}{x ^{2}} + \frac{c _{1}}{x ^{2}}

y = - \frac{3 ( e ^{x} x - e ^{x} )}{x ^{2}} + \frac{c _{1}}{x ^{2}}

What is the solution for x(dy)/(dx)+2y=-3e^x ?
The solution for x(dy)/(dx)+2y=-3e^x is y=-(3(e^xx-e^x))/(x^2)+(c_{1})/(x^2)