Internal problem ID [10338]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 1, First order differential equations. Section 1.1 First order equations. Exercises page
10
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {t^{2} x^{\prime \prime }-6 x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(t^2*diff(x(t),t$2)-6*x(t)=0,x(t), singsol=all)
\[ x \left (t \right ) = c_{1} t^{3}+\frac {c_{2}}{t^{2}} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 18
DSolve[t^2*x''[t]-6*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {c_2 t^5+c_1}{t^2} \\ \end{align*}