Internal problem ID [11681]
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 (vii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {x^{\prime }+5 x=t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(x(t),t)+5*x(t)=t,x(t), singsol=all)
\[ x \left (t \right ) = \frac {t}{5}-\frac {1}{25}+{\mathrm e}^{-5 t} c_{1} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 22
DSolve[x'[t]+5*x[t]==t,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {t}{5}+c_1 e^{-5 t}-\frac {1}{25} \]