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

Lösung

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

y = \frac{2 ( x ^{2} - 1 ) ^{\frac{3}{2}}}{3} + 1

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{2 ( x ^{2} - 1 ) ^{\frac{3}{2}}}{3} + 1

y = \frac{2 ( x ^{2} - 1 ) ^{\frac{3}{2}}}{3} + 1

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

\frac{d y}{d x} = e^{y}, y = 0, x = 1

x^{2} y^{^{'}} = (x + 7) y

y^{^{'}} - y^{2} e^{- 2 x} = 0

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