What is the solution for xy^'+3y=(4e^{2x})/(x^2) ?

The solution for xy^'+3y=(4e^{2x})/(x^2) is y=(2e^{2x})/(x^3)+(c_{1})/(x^3)

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xy^'+3y=(4e^{2x})/(x^2)

x y^{^{'}} + 3 y = \frac{4 e ^{2 x}}{x ^{2}}

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

Solution steps

x y^{'} (x) + 3 y = \frac{4 e ^{2 x}}{x ^{2}}

Solve linear ODE:

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

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

x \to 1 lim (\frac{2 x}{x - 1})

f (x) = 9 x^{5} (x^{3} - 2 x)

y^{^{''}} - 2 y^{^{'}} - 63 y = 0

n = 1 \sum \infty \frac{1}{n ^{- 1}}

\frac{d ^{2} y}{d ^{2} x} + \frac{4 d y}{d x} + 3 y = 0

What is the solution for xy^'+3y=(4e^{2x})/(x^2) ?
The solution for xy^'+3y=(4e^{2x})/(x^2) is y=(2e^{2x})/(x^3)+(c_{1})/(x^3)