65.4.5 problem 9.1 (v)

Internal problem ID [13735]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 9, First order linear equations and the integrating factor. Exercises page 86
Problem number : 9.1 (v)
Date solved : Tuesday, January 28, 2025 at 06:00:15 AM
CAS classification : [_linear]

\begin{align*} x^{\prime }+x \tanh \left (t \right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve(diff(x(t),t)+x(t)*tanh(t)=3,x(t), singsol=all)
 

\[ x \left (t \right ) = 3 \tanh \left (t \right )+\operatorname {sech}\left (t \right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 23

DSolve[D[x[t],t]+x[t]*Tanh[t]==3,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \text {sech}(t) \left (\int _1^t3 \cosh (K[1])dK[1]+c_1\right ) \]