Internal problem ID [2302]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with
Nonconstant Coefficients. page 567
Problem number: Problem 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+t y^{\prime }+25 y=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = \frac {3 \sqrt {3}}{2}, y^{\prime }\relax (1) = {\frac {15}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 22
dsolve([t^2*diff(y(t),t$2)+t*diff(y(t),t)+25*y(t)=0,y(1) = 3/2*3^(1/2), D(y)(1) = 15/2],y(t), singsol=all)
\[ y \relax (t ) = \frac {3 \sin \left (5 \ln \relax (t )\right )}{2}+\frac {3 \sqrt {3}\, \cos \left (5 \ln \relax (t )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 26
DSolve[{t^2*y''[t]+t*y'[t]+25*y[t]==0,{y[1]==3*Sqrt[3]/2,y'[1]==15/2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {3}{2} \left (\sin (5 \log (t))+\sqrt {3} \cos (5 \log (t))\right ) \\ \end{align*}