74.4.45 problem 45

Internal problem ID [15938]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 45
Date solved : Tuesday, January 28, 2025 at 08:23:35 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.058 (sec). Leaf size: 15

dsolve([diff(y(t),t)=sqrt(t)/y(t),y(0) = 2],y(t), singsol=all)
 

\[ y = \frac {2 \sqrt {9+3 t^{{3}/{2}}}}{3} \]

✓ Solution by Mathematica

Time used: 1.705 (sec). Leaf size: 23

DSolve[{D[y[t],t]==Sqrt[t]/y[t],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {2 \sqrt {t^{3/2}+3}}{\sqrt {3}} \]