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

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

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xy^'+3y=((2e^{-2x}))/(x^2)

x y^{^{'}} + 3 y = \frac{( 2 e ^{- 2 x} )}{x ^{2}}

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

Solution steps

x y^{'} (x) + 3 y = \frac{( 2 e ^{- 2 x} )}{x ^{2}}

Solve linear ODE:

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

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

x \to \infty lim (7 + \frac{1}{x})

x^{3} + y^{3} = 9 x y, (4, 2)

x \to - 1 lim (- 4 x^{9} - 2 x^{6} - x^{3})

\frac{d}{d x} (x + ln x^{2} - 4 x + 3)

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