Internal problem ID [1104]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page
203
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (x^{2}-4\right ) y^{\prime \prime }+4 y^{\prime } x +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve((x^2-4)*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x c_{1}+c_{2}}{x^{2}-4} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 20
DSolve[(x^2-4)*y''[x]+4*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x+c_1}{x^2-4} \\ \end{align*}