Internal problem ID [650]
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: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(t^2*diff(y(t),t$2)+ 7*t*diff(y(t),t)+10*y(t) = 0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1} \sin \left (\ln \relax (t )\right )}{t^{3}}+\frac {c_{2} \cos \left (\ln \relax (t )\right )}{t^{3}} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 22
DSolve[t^2*y''[t]+7*t*y'[t]+10*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_2 \cos (\log (t))+c_1 \sin (\log (t))}{t^3} \\ \end{align*}