What is the solution for (dy)/(dt)=sqrt(t)+t^2 ?

The solution for (dy)/(dt)=sqrt(t)+t^2 is y= 2/3 t^{3/2}+(t^3)/3+c_{1}

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(dy)/(dt)=sqrt(t)+t^2

\frac{d y}{d t} = t + t^{2}

y = \frac{2}{3} t^{\frac{3}{2}} + \frac{t ^{3}}{3} + c_{1}

Solution steps

\frac{d y}{d t} = t + t^{2}

Substitute

\frac{d y}{d t}

with

y^{'} (t)

y^{^{'}} (t) = t + t^{2}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int t + t^{2} d t

\int t + t^{2} d t = \frac{2}{3} t^{\frac{3}{2}} + \frac{t ^{3}}{3} + c_{1}

y = \frac{2}{3} t^{\frac{3}{2}} + \frac{t ^{3}}{3} + c_{1}

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What is the solution for (dy)/(dt)=sqrt(t)+t^2 ?
The solution for (dy)/(dt)=sqrt(t)+t^2 is y= 2/3 t^{3/2}+(t^3)/3+c_{1}