Internal problem ID [11381]
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 1.3.1 Separable equations. Exercises
page 26
Problem number: 4(f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (1+t \right ) x^{\prime }+x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve((1+t)*diff(x(t),t)+x(t)^2=0,x(t), singsol=all)
\[ x \left (t \right ) = \frac {1}{\ln \left (t +1\right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.161 (sec). Leaf size: 21
DSolve[(1+t)*x'[t]+x[t]^2==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{\log (t+1)-c_1} \\ x(t)\to 0 \\ \end{align*}