Internal problem ID [648]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation ,
page 164
Problem number: 40.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }-t y^{\prime }+5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 21
dsolve(t^2*diff(y(t),t$2)- t*diff(y(t),t)+5*y(t) = 0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} t \sin \left (2 \ln \relax (t )\right )+c_{2} t \cos \left (2 \ln \relax (t )\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 24
DSolve[t^2*y''[t]-t*y'[t]+5*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t (c_2 \cos (2 \log (t))+c_1 \sin (2 \log (t))) \\ \end{align*}