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Popular Calculus >

y^'=\sqrt[3]{y/(x-1)}

Solution

Solution

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

Solution steps

Solve separable ODE:

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

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

Graph

Popular Examples

y^'+6y=4,y(0)=0

(dy)/(dx)=((ln(x))^6)/(xy^2)

(dy)/(dx)=(x^2+1)/(y^2+1),y(2)=2

y'(t)=y(y+1)^2,y(0)=1

Frequently Asked Questions (FAQ)

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