e^xy^'=2(x+1)y^2

Lösung

e^{x} y^{^{'}} = 2 (x + 1) y^{2}

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

Schritte zur Lösung

e^{x} y^{'} (x) = 2 (x + 1) y^{2}

Solve separable ODE:

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

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

x + 2 y (- \frac{1}{y ^{^{'}}}) = 0

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

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

x^{2} (y^{^{'}})^{1} - 3 x y^{^{'}} + 16 y = 0

\frac{d y}{d x} = 100 - \frac{y}{100}