sqrt(1-y^2)dx=(1+x^2)ydy,y(0)=0

Lösung

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

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

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

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

\frac{d y}{d x} - 2 y = y, y = e, x = 0

y^{^{'}} - 8 x y = 0