(dy)/(dx)=7x+2xy,y(0)=1

Lösung

\frac{d y}{d x} = 7 x + 2 x y, y (0) = 1

y = \frac{9 e ^{x^{2}}}{2} - \frac{7}{2}

Schritte zur Lösung

\frac{d y}{d x} = 7 x + 2 x y

Solve separable ODE:

y = \frac{9 e ^{x^{2}}}{2} - \frac{7}{2}

y = \frac{9 e ^{x^{2}}}{2} - \frac{7}{2}

\frac{d x}{d t} = 3 x + 1

e^{x} y^{^{'}} = 2 (x + 1) y^{2}

x + 2 y (- \frac{1}{y ^{^{'}}}) = 0

(1 + x^{2}) (\frac{d y}{d x}) + x e^{- y} = 0

y - 2 x y^{^{'}} = 0