Internal problem ID [11999]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{\prime }+x \tanh \left (t \right )=3} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.094 (sec). Leaf size: 15
DSolve[x'[t]+x[t]*Tanh[t]==3,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \text {sech}(t) (3 \sinh (t)+c_1) \]