20.10.10 problem Problem 23

Internal problem ID [3782]
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
Date solved : Monday, January 27, 2025 at 08:02:13 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+25 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=\frac {3 \sqrt {3}}{2}\\ y^{\prime }\left (1\right )&={\frac {15}{2}} \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)
 

\[ y = \frac {3 \sin \left (5 \ln \left (t \right )\right )}{2}+\frac {3 \sqrt {3}\, \cos \left (5 \ln \left (t \right )\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 26

DSolve[{t^2*D[y[t],{t,2}]+t*D[y[t],t]+25*y[t]==0,{y[1]==3*Sqrt[3]/2,Derivative[1][y][1]==15/2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {3}{2} \left (\sin (5 \log (t))+\sqrt {3} \cos (5 \log (t))\right ) \]