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Popular >

(dy)/(dx)=5(y-2)^{3/5}

Solution

\frac{d y}{d x} = 5 (y - 2)^{\frac{3}{5}}

Solution

y = \frac{( 100000 x ^{5} + 100000 c _{1} x ^{4} + 40000 c _{1}^{2} x ^{3} + 8000 c _{1}^{3} x ^{2} + 800 c _{1}^{4} x + 32 c _{1}^{5} ) ^{\frac{1}{2}}}{25 \cdot 5 ^{\frac{1}{2}}} + 2, y = - \frac{( 100000 x ^{5} + 100000 c _{1} x ^{4} + 40000 c _{1}^{2} x ^{3} + 8000 c _{1}^{3} x ^{2} + 800 c _{1}^{4} x + 32 c _{1}^{5} ) ^{\frac{1}{2}}}{25 \cdot 5 ^{\frac{1}{2}}} + 2

Solution steps

\frac{d y}{d x} = 5 (y - 2)^{\frac{3}{5}}

Solve separable ODE:

y = \frac{( 100000 x ^{5} + 100000 c _{1} x ^{4} + 40000 c _{1}^{2} x ^{3} + 8000 c _{1}^{3} x ^{2} + 800 c _{1}^{4} x + 32 c _{1}^{5} ) ^{\frac{1}{2}}}{25 \cdot 5 ^{\frac{1}{2}}} + 2, y = - \frac{( 100000 x ^{5} + 100000 c _{1} x ^{4} + 40000 c _{1}^{2} x ^{3} + 8000 c _{1}^{3} x ^{2} + 800 c _{1}^{4} x + 32 c _{1}^{5} ) ^{\frac{1}{2}}}{25 \cdot 5 ^{\frac{1}{2}}} + 2

y = \frac{( 100000 x ^{5} + 100000 c _{1} x ^{4} + 40000 c _{1}^{2} x ^{3} + 8000 c _{1}^{3} x ^{2} + 800 c _{1}^{4} x + 32 c _{1}^{5} ) ^{\frac{1}{2}}}{25 \cdot 5 ^{\frac{1}{2}}} + 2, y = - \frac{( 100000 x ^{5} + 100000 c _{1} x ^{4} + 40000 c _{1}^{2} x ^{3} + 8000 c _{1}^{3} x ^{2} + 800 c _{1}^{4} x + 32 c _{1}^{5} ) ^{\frac{1}{2}}}{25 \cdot 5 ^{\frac{1}{2}}} + 2

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Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)=5(y-2)^{3/5} ?
The solution for (dy)/(dx)=5(y-2)^{3/5} is