y^'=(2x)/y ,y(1)=-2

Lösung

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

y = - 2 x^{2} + 2

Schritte zur Lösung

y^{'} (x) = \frac{2 x}{y}

Solve separable ODE:

y = - 2 x^{2} + 2

y = - 2 x^{2} + 2

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

(t^{2} + 4) x^{^{'}} = 2 t x

(x^{2} + 4) y^{^{'}} + 8 x y = 2 x

\frac{d y}{d t} = \frac{( 50 - y )}{10}

\frac{d y}{d x} = 3 x y, y \neq = 0