Internal problem ID [11490]
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 2.4.1 Cauchy-Euler equations.
Exercises page 120
Problem number: 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {t^{2} x^{\prime \prime }+3 x^{\prime } t +x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(t^2*diff(x(t),t$2)+3*t*diff(x(t),t)+x(t)=0,x(t), singsol=all)
\[ x \left (t \right ) = \frac {c_{1}}{t}+\frac {c_{2} \ln \left (t \right )}{t} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 17
DSolve[t^2*x''[t]+3*t*x'[t]+x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {c_2 \log (t)+c_1}{t} \]