y^'=-2xe^y,y(2)=5

Lösung

y^{^{'}} = - 2 x e^{y}, y (2) = 5

y = - ln (x^{2} + \frac{1}{e ^{5}} - 4)

Schritte zur Lösung

y^{'} (x) = - 2 x e^{y}

Solve separable ODE:

y = - ln (x^{2} + \frac{1}{e ^{5}} - 4)

y = - ln (x^{2} + \frac{1}{e ^{5}} - 4)

d y = x^{4} (1 - 5 y) d x

y^{^{'}} + y - 1 = 0

7 y y^{^{'}} = x, y (7) = 3

y^{^{'}} - \frac{x}{5 y ^{4}} = 0, y (0) = 2, y (2) = a

\frac{d y}{d x} = y^{2} - 25