(e^x+1)(dy)/(dx)+ye^x-y=0

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

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

\frac{d y}{d x} - y = 6, y = 2, x = 0

31 e^{x - 2 y} = 3 \frac{d x}{d y}

2 x y^{^{'}} = 7 y

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