Internal problem ID [11491]
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(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(t*diff(x(t),t$2)+4*diff(x(t),t)+2/t*x(t)=0,x(t), singsol=all)
\[ x \left (t \right ) = \frac {c_{1}}{t}+\frac {c_{2}}{t^{2}} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 16
DSolve[t*x''[t]+4*x'[t]+2/t*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {c_2 t+c_1}{t^2} \]