Internal problem ID [11420]
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 1.4.1. Integrating factors. Exercises
page 41
Problem number: 2(f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (t^{2}+1\right ) x^{\prime }+3 t x=6 t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((t^2+1)*diff(x(t),t)=-3*t*x(t)+6*t,x(t), singsol=all)
\[ x \left (t \right ) = 2+\frac {c_{1}}{\left (t^{2}+1\right )^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 24
DSolve[(t^2+1)*x'[t]==-3*t*x[t]+6*t,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 2+\frac {c_1}{\left (t^2+1\right )^{3/2}} x(t)\to 2 \end{align*}