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Popular >

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}

Popular Examples

(dy)/(dx)=5x+15y

\frac{d y}{d x} = 5 x + 15 y

f(x)= x/(4x+3ln(x))

f (x) = \frac{x}{4 x + 3 ln ( x )}

slope of y=(-4x^2+12)/(2x+2)slope

y = \frac{- 4 x ^{2} + 12}{2 x + 2}

derivative of (2x-3x^3tan(x))

\frac{d}{d x} ((2 x - 3 x^{3}) tan (x))

derivative of arcsin(e^{-x})

\frac{d}{d x} (arcsin (e^{- x}))

Frequently Asked Questions (FAQ)

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