63.1.3 problem 3

Internal problem ID [13027]
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 : 3
Date solved : Tuesday, January 28, 2025 at 04:49:38 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=-x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 9

dsolve(diff(x(t),t)=-x(t)^2,x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {1}{t +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.039 (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*}