y^'=3xe^y,y(0)=0

Lösung

y^{^{'}} = 3 x e^{y}, y (0) = 0

y = - ln (- \frac{3 x ^{2}}{2} + 1)

Schritte zur Lösung

y^{'} (x) = 3 x e^{y}

Solve separable ODE:

y = - ln (- \frac{3 x ^{2}}{2} + 1)

y = - ln (- \frac{3 x ^{2}}{2} + 1)

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

\frac{d y}{d x} = y (5 x^{2} + 1)

y + y^{^{'}} = 0

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

\frac{d y}{d x} + x e^{y} = 0