y^'=(64xy)^{1/3}

Lösung

y^{^{'}} = (64 x y)^{\frac{1}{3}}

y = \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}, y = - \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}

Schritte zur Lösung

y^{'} (x) = (64 x y)^{\frac{1}{3}}

Solve separable ODE:

y = \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}, y = - \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}

y = \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}, y = - \frac{2 2 27 x ^{4} + 27 c _{1} x ^{\frac{8}{3}} + 9 c _{1}^{2} x ^{\frac{4}{3}} + c _{1}^{3}}{3 3}

d er i v a t i v e y = \frac{x}{2}

d er i v a t i v e \frac{9}{x ^{3}}

\int \frac{( 3 x ^{2} + 7 x + 3 )}{x ( x + 1 ) ^{2}} d x

\frac{\partial}{\partial x} (\frac{sin ( y )}{x ^{2} + 1})

\int 10 x - x^{2} d x