What is the solution for (dy)/(dt)=t*sqrt(y) ?

The solution for (dy)/(dt)=t*sqrt(y) is y=(t^4}{16}+\frac{c_{1}t^2)/4+(c_{1}^2)/4

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(dy)/(dt)=t*sqrt(y)

\frac{d y}{d t} = t \cdot y

y = \frac{t ^{4}}{16} + \frac{c _{1} t ^{2}}{4} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d t} = t \cdot y

Solve separable ODE:

y = \frac{t ^{4}}{16} + \frac{c _{1} t ^{2}}{4} + \frac{c _{1}^{2}}{4}

y = \frac{t ^{4}}{16} + \frac{c _{1} t ^{2}}{4} + \frac{c _{1}^{2}}{4}

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What is the solution for (dy)/(dt)=t*sqrt(y) ?
The solution for (dy)/(dt)=t*sqrt(y) is y=(t^4}{16}+\frac{c_{1}t^2)/4+(c_{1}^2)/4