y^'=1+x+y+xy,y(0)=0

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

x^{3} + 4 y \frac{d y}{d x} = 0

\frac{d y}{d x} = - \frac{4}{8} x^{9} y^{8}

y y^{^{'}} + 2 sin (2 x) = 0

y^{^{'}} = 120 - 2 y

y^{^{'}} = 135 x^{2} y + 18 x y + 30 x^{2} + 4 x