xyy^'=e^y

Lösung

x y y^{^{'}} = e^{y}

y = - W (\frac{ln ( x ) + c _{1}}{e}) - 1

Schritte zur Lösung

x y y^{'} (x) = e^{y}

Solve separable ODE:

y = - W (\frac{ln ( x ) + c _{1}}{e}) - 1

y = - W (\frac{ln ( x ) + c _{1}}{e}) - 1

y^{^{'}} + a \cdot y^{2} = b

\frac{d y}{d x} = - 4 x^{3} y

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

4 y^{^{'}} - 2 e^{3 x} y = 0, y (0) = 6

cos^{2} (x) \frac{d y}{d x} = y + 3