4.5 problem 9.1 (v)

Internal problem ID [11679]

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: 15

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

\[ x \left (t \right ) = \frac {3 \sinh \left (t \right )+c_{1}}{\cosh \left (t \right )} \]

Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 15

DSolve[x'[t]+x[t]*Tanh[t]==3,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \text {sech}(t) (3 \sinh (t)+c_1) \]