What is the solution for 1/x (dy)/(dx)+2y-e^{-x^2}=0 ?

The solution for 1/x (dy)/(dx)+2y-e^{-x^2}=0 is y=(x^2)/(2e^{x^2)}+(c_{1})/(e^{x^2)}

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1/x (dy)/(dx)+2y-e^{-x^2}=0

\frac{1}{x} \frac{d y}{d x} + 2 y - e^{- x^{2}} = 0

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

Solution steps

\frac{1}{x} \frac{d y}{d x} + 2 y - e^{- x^{2}} = 0

Solve linear ODE:

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

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

x \to 0 lim (\frac{\frac{6}{x + 6} - 1}{x})

x \to 10 lim (- 15)

y = 3 e^{x}

\frac{0.1 s}{s ^{2} + 10 s + 9.8}

\int 5 x x + 2 d x

What is the solution for 1/x (dy)/(dx)+2y-e^{-x^2}=0 ?
The solution for 1/x (dy)/(dx)+2y-e^{-x^2}=0 is y=(x^2)/(2e^{x^2)}+(c_{1})/(e^{x^2)}