74.3.32 problem 27

Internal problem ID [15892]
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 : 27
Date solved : Tuesday, January 28, 2025 at 08:17:33 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 15

dsolve([diff(y(t),t)=-t/y(t),y(0) = 1/2],y(t), singsol=all)
 

\[ y = \frac {\sqrt {-4 t^{2}+1}}{2} \]

✓ Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 20

DSolve[{D[y[t],t]==-t/y[t],{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} \sqrt {1-4 t^2} \]