Internal problem ID [11489]
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(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{\prime \prime }-\frac {4 x}{t^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(x(t),t$2)=4/t^2*x(t),x(t), singsol=all)
\[ x \left (t \right ) = c_{1} t^{\frac {1}{2}+\frac {\sqrt {17}}{2}}+c_{2} t^{\frac {1}{2}-\frac {\sqrt {17}}{2}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 34
DSolve[x''[t]==4/t^2*x[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to t^{\frac {1}{2}-\frac {\sqrt {17}}{2}} \left (c_2 t^{\sqrt {17}}+c_1\right ) \]