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Popular >

(dy)/(dx)=(xy)^{1/3}

Solution

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

Solution

y = \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6}, y = - \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6}

Solution steps

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

Solve separable ODE:

y = \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6}, y = - \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6}

y = \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6}, y = - \frac{27 x ^{4} + 108 c _{1} x ^{\frac{8}{3}} + 144 c _{1}^{2} x ^{\frac{4}{3}} + 64 c _{1}^{3}}{6 6}

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Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)=(xy)^{1/3} ?
The solution for (dy)/(dx)=(xy)^{1/3} is