63.5.12 problem 2(f)

Internal problem ID [13086]
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)
Date solved : Tuesday, January 28, 2025 at 04:51:50 AM
CAS classification : [_separable]

\begin{align*} \left (t^{2}+1\right ) x^{\prime }&=-3 x t +6 t \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve((t^2+1)*diff(x(t),t)=-3*t*x(t)+6*t,x(t), singsol=all)
 

\[ x \left (t \right ) = 2+\frac {c_{1}}{\left (t^{2}+1\right )^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 24

DSolve[(t^2+1)*D[x[t],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*}