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

The solution for 1/x*(dy)/(dx)+2y-e^{-x^2}=0,y(1)= 2/e is y=(x^2)/(2e^{x^2)}+3/(2e^{x^2)}

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

\frac{1}{x} \cdot \frac{d y}{d x} + 2 y - e^{- x^{2}} = 0, y (1) = \frac{2}{e}

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

Solution steps

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

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (lo g_{e} (x))

x \to - 2 + lim (f (x))

\int a e^{- a x} d x

(x^{3} cos (x))^{^{'}}

\int \frac{1}{16 x ^{4} - 8 x ^{2} + 1} d x

What is the solution for 1/x*(dy)/(dx)+2y-e^{-x^2}=0,y(1)= 2/e ?
The solution for 1/x*(dy)/(dx)+2y-e^{-x^2}=0,y(1)= 2/e is y=(x^2)/(2e^{x^2)}+3/(2e^{x^2)}