sqrt(1-y^2)dx=(1+x^2)ydy

Lösung

1 - y^{2} d x = (1 + x^{2}) y d y

y = - arctan^{2} (x) - 2 c_{1} arctan (x) - c_{1}^{2} + 1, y = - - arctan^{2} (x) - 2 c_{1} arctan (x) - c_{1}^{2} + 1

Schritte zur Lösung

1 - y^{2} d x = (1 + x^{2}) y d y

Solve separable ODE:

y = - arctan^{2} (x) - 2 c_{1} arctan (x) - c_{1}^{2} + 1, y = - - arctan^{2} (x) - 2 c_{1} arctan (x) - c_{1}^{2} + 1

y = - arctan^{2} (x) - 2 c_{1} arctan (x) - c_{1}^{2} + 1, y = - - arctan^{2} (x) - 2 c_{1} arctan (x) - c_{1}^{2} + 1

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

\frac{d v}{d t} = - 0.4 v

2 x d x + x^{2} cot (y) d y = 0

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

\frac{d x}{d t} = 100 - \frac{x}{100}