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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Solve separable ODE:

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

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

Graph

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(x-1)^3(dy)/(dx)+4(x-1)^2y=x+1

Frequently Asked Questions (FAQ)

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