yy^'=xsqrt(1-y^2)

Lösung

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

y = \frac{- x ^{4} - 4 c _{1} x ^{2} - 4 c _{1}^{2} + 4}{2}, y = - \frac{- x ^{4} - 4 c _{1} x ^{2} - 4 c _{1}^{2} + 4}{2}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{- x ^{4} - 4 c _{1} x ^{2} - 4 c _{1}^{2} + 4}{2}, y = - \frac{- x ^{4} - 4 c _{1} x ^{2} - 4 c _{1}^{2} + 4}{2}

y = \frac{- x ^{4} - 4 c _{1} x ^{2} - 4 c _{1}^{2} + 4}{2}, y = - \frac{- x ^{4} - 4 c _{1} x ^{2} - 4 c _{1}^{2} + 4}{2}

d v = cos (x) d x

y^{^{'}} \cdot sin (x) + y = 0

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

5 y^{4} d y = 6 x d x

\frac{d y}{d x} - 2 y = 3