Internal problem ID [11492]
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(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {t^{2} x^{\prime \prime }-7 x^{\prime } t +16 x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(t^2*diff(x(t),t$2)-7*t*diff(x(t),t)+16*x(t)=0,x(t), singsol=all)
\[ x \left (t \right ) = t^{4} c_{1} +c_{2} t^{4} \ln \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 18
DSolve[t^2*x''[t]-7*t*x'[t]+16*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to t^4 (4 c_2 \log (t)+c_1) \]