73.13.24 problem 20.2 (f)

Internal problem ID [15402]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.2 (f)
Date solved : Tuesday, January 28, 2025 at 07:54:37 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=9\\ y^{\prime }\left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 23

dsolve([x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+13*y(x)=0,y(1) = 9, D(y)(1) = 3],y(x), singsol=all)
 

\[ y = x^{2} \left (-5 \sin \left (3 \ln \left (x \right )\right )+9 \cos \left (3 \ln \left (x \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 24

DSolve[{x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+13*y[x]==0,{y[1]==9,Derivative[1][y][1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (9 \cos (3 \log (x))-5 \sin (3 \log (x))) \]