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Popular Calculus >

y^'=y^{1/3}

Solution

y^{^{'}} = y^{\frac{1}{3}}

Solution

y = \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}, y = - \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}

Solution steps

y^{'} (t) = y^{\frac{1}{3}}

Solve separable ODE:

y = \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}, y = - \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}

y = \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}, y = - \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}

Graph

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Frequently Asked Questions (FAQ)

What is the solution for y^'=y^{1/3} ?
The solution for y^'=y^{1/3} is