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Popular >

y^'=5t^3y^{1/5}

Solution

y^{^{'}} = 5 t^{3} y^{\frac{1}{5}}

Solution

y = \frac{4 3125 t ^{20} + 12500 c _{1} t ^{16} + 20000 c _{1}^{2} t ^{12} + 16000 c _{1}^{3} t ^{8} + 6400 c _{1}^{4} t ^{4} + 1024 c _{1}^{5}}{5 4 5}, y = - \frac{4 3125 t ^{20} + 12500 c _{1} t ^{16} + 20000 c _{1}^{2} t ^{12} + 16000 c _{1}^{3} t ^{8} + 6400 c _{1}^{4} t ^{4} + 1024 c _{1}^{5}}{5 4 5}

Solution steps

y^{'} (t) = 5 t^{3} y^{\frac{1}{5}}

Solve separable ODE:

y = \frac{4 3125 t ^{20} + 12500 c _{1} t ^{16} + 20000 c _{1}^{2} t ^{12} + 16000 c _{1}^{3} t ^{8} + 6400 c _{1}^{4} t ^{4} + 1024 c _{1}^{5}}{5 4 5}, y = - \frac{4 3125 t ^{20} + 12500 c _{1} t ^{16} + 20000 c _{1}^{2} t ^{12} + 16000 c _{1}^{3} t ^{8} + 6400 c _{1}^{4} t ^{4} + 1024 c _{1}^{5}}{5 4 5}

y = \frac{4 3125 t ^{20} + 12500 c _{1} t ^{16} + 20000 c _{1}^{2} t ^{12} + 16000 c _{1}^{3} t ^{8} + 6400 c _{1}^{4} t ^{4} + 1024 c _{1}^{5}}{5 4 5}, y = - \frac{4 3125 t ^{20} + 12500 c _{1} t ^{16} + 20000 c _{1}^{2} t ^{12} + 16000 c _{1}^{3} t ^{8} + 6400 c _{1}^{4} t ^{4} + 1024 c _{1}^{5}}{5 4 5}

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the solution for y^'=5t^3y^{1/5} ?
The solution for y^'=5t^3y^{1/5} is