74.3.7 problem 7

Internal problem ID [15867]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 08:10:45 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=y \sqrt {t} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 18

dsolve([diff(y(t),t)=y(t)*sqrt(t),y(1) = 1],y(t), singsol=all)
 

\[ y = {\mathrm e}^{\frac {2 \left (\sqrt {t}-1\right ) \left (t +\sqrt {t}+1\right )}{3}} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 18

DSolve[{D[y[t],t]==y[t]*Sqrt[t],{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{\frac {2}{3} \left (t^{3/2}-1\right )} \]