e^yy^'-x^2=0,y(0)=0

Lösung

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

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

Schritte zur Lösung

e^{y} y^{'} (x) - x^{2} = 0

Solve separable ODE:

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

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

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

y^{^{'}} - (tan (x)) y = 0

y^{^{'}} + 4 x y - \frac{8 x}{y ^{3}} = 0

\frac{d y}{d x} = \frac{3 x - 5}{y - 2}

y^{^{'}} = 4 x^{2} y + 5 x y, y (1) = 1