x^2yy^'=(y^2-1)^{3/2}

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{d}{d x} (x ln (\frac{1}{x}))

d er i v a t i v e y = 2

\frac{d x}{d t} = t x^{\frac{1}{3}}, x (1) = 1

\int_{0}^{4} \frac{x}{9 + x ^{2}} d x

\frac{d}{d x} (10 x^{2} e^{x})