49.14.1 problem 1

Internal problem ID [7684]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 3. Linear equations with variable coefficients. Page 124
Problem number : 1
Date solved : Monday, January 27, 2025 at 03:09:47 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

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

\[ y = \frac {c_{2} x^{3}+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 18

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

\[ y(x)\to \frac {c_2 x^3+c_1}{x} \]