Chapter 5 - The Integral - 5.3 The Indefinite Integral - Exercises - Page 253: 51

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

$\frac{dy}{dt}=\sqrt t;$ $y(1)=1$ $dy=\sqrt tdt$ $\int dy=\int t^{\frac{1}{2}}dt$ $y=\frac{2t^{\frac{3}{2}}}{3}+C$ $1=\frac{2}{3}+C$ $C=\frac{1}{3}$ $y=\frac{2t^{\frac{3}{2}}}{3}+\frac{1}{3}$