73.9.14 problem 14.2 (d)

Internal problem ID [15275]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.2 (d)
Date solved : Tuesday, January 28, 2025 at 07:51:27 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

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

\[ y = c_{1} \sqrt {x}+c_{2} x \]

✓ Solution by Mathematica

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

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

\[ y(x)\to c_1 \sqrt {x}+c_2 x \]