Internal problem ID [11484]
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(g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {t^{2} x^{\prime \prime }+t x^{\prime }=0} \] With initial conditions \begin {align*} [x \left (1\right ) = 0, x^{\prime }\left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 8
dsolve([t^2*diff(x(t),t$2)+t*diff(x(t),t)=0,x(1) = 0, D(x)(1) = 2],x(t), singsol=all)
\[ x \left (t \right ) = 2 \ln \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 9
DSolve[{t^2*x''[t]+t*x'[t]==0,{x[1]==0,x'[1]==2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to 2 \log (t) \]