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Popular Calculus >

(dy)/(dt)=y^{1/3}t^{2/5}

Solution

\frac{d y}{d t} = y^{\frac{1}{3}} t^{\frac{2}{5}}

Solution

y = \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}, y = - \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}

Solution steps

\frac{d y}{d t} = y^{\frac{1}{3}} t^{\frac{2}{5}}

Solve separable ODE:

y = \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}, y = - \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}

y = \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}, y = - \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}

Graph

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Frequently Asked Questions (FAQ)

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