Internal problem ID [10393]
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: 3(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{\prime }+\frac {5 x}{t}-1-t=0} \] With initial conditions \begin {align*} [x \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([diff(x(t),t)+(5/t)*x(t)=1+t,x(1) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {t^{2}}{7}+\frac {t}{6}+\frac {29}{42 t^{5}} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 23
DSolve[{x'[t]+(5/t)*x[t]==1+t,{x[1]==1}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {(6 t+7) t^6+29}{42 t^5} \\ \end{align*}