Internal problem ID [11430]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x^{\prime \prime }+x^{\prime }=3 t} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve(diff(x(t),t$2)+diff(x(t),t)=3*t,x(t), singsol=all)
\[ x \left (t \right ) = -{\mathrm e}^{-t} c_{1} +\frac {3 t^{2}}{2}-3 t +c_{2} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 27
DSolve[x''[t]+x'[t]==3*t,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {3 t^2}{2}-3 t-c_1 e^{-t}+c_2 \]