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

Lösung

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

y = - \frac{4 e ^{x^{2}}}{2 e ^{x^{2}} - 1 - 2 e} - \frac{2}{2 e ^{x^{2}} - 1 - 2 e} + \frac{4 e}{2 e ^{x^{2}} - 1 - 2 e}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{4 e ^{x^{2}}}{2 e ^{x^{2}} - 1 - 2 e} - \frac{2}{2 e ^{x^{2}} - 1 - 2 e} + \frac{4 e}{2 e ^{x^{2}} - 1 - 2 e}

y = - \frac{4 e ^{x^{2}}}{2 e ^{x^{2}} - 1 - 2 e} - \frac{2}{2 e ^{x^{2}} - 1 - 2 e} + \frac{4 e}{2 e ^{x^{2}} - 1 - 2 e}

y^{^{'}} = y ln (y) cot (x)

\frac{d y}{d t} = - \frac{y}{( \frac{4320}{7} )}

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

y^{^{'}} + \frac{y}{3} = 5, y (- 1) = 0

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