What is the solution for xy^'+2y=3e^x ?

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

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xy^'+2y=3e^x

x y^{^{'}} + 2 y = 3 e^{x}

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

Solution steps

x y^{'} (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}}

- \frac{3}{5000} r^{3} + \frac{9}{50} r^{2}

\frac{( x ^{2} - x - 2 )}{( x ^{2} - 6 x + 9 )}

x \to 9 + lim (x^{2} + 5 x + 7)

f (x) = x^{3}, (- 1, - 1)

\frac{d y}{d x} = y x

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