Internal problem ID [11493]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 2, Second order linear equations. Section 2.4.2 Variation of parameters.
Exercises page 124
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x^{\prime \prime }+\frac {x^{\prime }}{t}=a} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(x(t),t$2)+1/t*diff(x(t),t)=a,x(t), singsol=all)
\[ x \left (t \right ) = \frac {a \,t^{2}}{4}+c_{1} \ln \left (t \right )+c_{2} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 21
DSolve[x''[t]+1/t*x'[t]==a,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {a t^2}{4}+c_1 \log (t)+c_2 \]