49.14.3 problem 3

Internal problem ID [7686]
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 : 3
Date solved : Monday, January 27, 2025 at 03:09:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+(2+x^2)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 37

DSolve[x^2*D[y[x],{x,2}]+4*x*D[y[x],x]+(2+x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 c_1 e^{-i x}-i c_2 e^{i x}}{2 x^2} \]