Internal problem ID [11483]
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(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x=0} \] With initial conditions \begin {align*} [x \left (1\right ) = 0, x^{\prime }\left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve([t^2*diff(x(t),t$2)+3*t*diff(x(t),t)-8*x(t)=0,x(1) = 0, D(x)(1) = 2],x(t), singsol=all)
\[ x \left (t \right ) = \frac {t^{6}-1}{3 t^{4}} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 17
DSolve[{t^2*x''[t]+3*t*x'[t]-8*x[t]==0,{x[1]==0,x'[1]==2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {t^6-1}{3 t^4} \]