63.12.7 problem 2

Internal problem ID [13169]
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
Date solved : Tuesday, January 28, 2025 at 05:11:52 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{t}&=a \end{align*}

✓ Solution by Maple

Time used: 0.001 (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: 0.031 (sec). Leaf size: 21

DSolve[D[x[t],{t,2}]+1/t*D[x[t],t]==a,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {a t^2}{4}+c_1 \log (t)+c_2 \]