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

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

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

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

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

Solution steps

x y^{'} (x) + 2 y = e^{x^{2}}

Solve linear ODE:

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

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

\frac{d}{d x} (- 2 cot (x) csc (x))

2 x^{2} - 5

h (x) = (x - 2) (2 x + 3)

\int 3 - e^{2 x} d x

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

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