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Popular >

y^'=3x(y-1)^{1/3}

Solution

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

Solution

y = \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1, y = - \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1

Solution steps

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

Solve separable ODE:

y = \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1, y = - \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1

y = \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1, y = - \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1

Popular Examples

area 10x-5x^2,x=\sqrt[3]{4},x=2 area

(\partial)/(\partial x)(3x*e^{2x+y^2})

\frac{\partial}{\partial x} (3 x \cdot e^{2 x + y^{2}})

derivative of xsqrt(3-2x^2)

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

integral of u/(sqrt(u^2-1))

\int \frac{u}{u ^{2} - 1} d u

(dN)/(dt)=(te^t)/(N^2)

\frac{d N}{d t} = \frac{t e ^{t}}{N ^{2}}

Frequently Asked Questions (FAQ)

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