xy-y(dy)/(dx)=2x,y(-1)=3

Lösung

x y - y \frac{d y}{d x} = 2 x, y (- 1) = 3

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

y^{^{'}} = \frac{8 y}{x}

\frac{d y}{d x} = - \frac{3}{8} x^{4} y^{4}

y y^{^{'}} + x e^{x^{2}} = 0

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

x y \frac{d y}{d x} = x^{2} + 1