73.13.1 problem 20.1 (a)

Internal problem ID [15379]
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 : 20.1 (a)
Date solved : Tuesday, January 28, 2025 at 07:53:54 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
 

\[ y = x^{2} \left (c_{2} x^{2}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \left (c_2 x^2+c_1\right ) \]