63.1.2 problem 1(b)

Internal problem ID [13026]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.1 First order equations. Exercises page 10
Problem number : 1(b)
Date solved : Tuesday, January 28, 2025 at 04:49:34 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(x(t),t)=-t/x(t),x(t), singsol=all)
 

\begin{align*} x \left (t \right ) &= \sqrt {-t^{2}+c_{1}} \\ x \left (t \right ) &= -\sqrt {-t^{2}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 39

DSolve[D[x[t],t]==-t/x[t],x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -\sqrt {-t^2+2 c_1} \\ x(t)\to \sqrt {-t^2+2 c_1} \\ \end{align*}