Internal problem ID [11749]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 19, CauchyEuler equations. Exercises page 174
Problem number: 19.1 (x).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {t^{2} x^{\prime \prime }+3 x^{\prime } t +13 x=0} \] With initial conditions \begin {align*} [x \left (1\right ) = -1, x^{\prime }\left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 32
dsolve([t^2*diff(x(t),t$2)+3*t*diff(x(t),t)+13*x(t)=0,x(1) = -1, D(x)(1) = 2],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\sqrt {3}\, \sin \left (2 \sqrt {3}\, \ln \left (t \right )\right )-6 \cos \left (2 \sqrt {3}\, \ln \left (t \right )\right )}{6 t} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 41
DSolve[{t^2*x''[t]+3*t*x'[t]+13*x[t]==0,{x[1]==-1,x'[1]==2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {\sqrt {3} \sin \left (2 \sqrt {3} \log (t)\right )-6 \cos \left (2 \sqrt {3} \log (t)\right )}{6 t} \]