ysqrt(1-x^2)y^'+sqrt(1-y^2)=0

Lösung

y 1 - x^{2} y^{^{'}} + 1 - y^{2} = 0

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

y^{^{'}} = y (1 - \frac{y}{3})

x^{^{'}} = - 100 x

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

6 y^{^{'}} + y = 0

y^{^{'}} + 3 x^{2} y = x^{2}, y (0) = 1