Internal problem ID [10332]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }+\frac {t}{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (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: 0.086 (sec). Leaf size: 39
DSolve[x'[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*}