(dy)/(dx)=x+2xy,y(0)=3

Lösung

\frac{d y}{d x} = x + 2 x y, y (0) = 3

y = \frac{7 e ^{x^{2}}}{2} - \frac{1}{2}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{7 e ^{x^{2}}}{2} - \frac{1}{2}

y = \frac{7 e ^{x^{2}}}{2} - \frac{1}{2}

e^{x} d x - y d y = 0

y y^{^{'}} = e^{2 x} + c

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

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

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