Internal problem ID [11485]
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(h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {t^{2} x^{\prime \prime }-t x^{\prime }+2 x=0} \] With initial conditions \begin {align*} [x \left (1\right ) = 0, x^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve([t^2*diff(x(t),t$2)-t*diff(x(t),t)+2*x(t)=0,x(1) = 0, D(x)(1) = 1],x(t), singsol=all)
\[ x \left (t \right ) = t \sin \left (\ln \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 10
DSolve[{t^2*x''[t]-t*x'[t]+2*x[t]==0,{x[1]==0,x'[1]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to t \sin (\log (t)) \]