Internal problem ID [1092]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -5, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 17
dsolve([(x^2-1)*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=0,y(0) = -5, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {-x +5}{x^{2}-1} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 18
DSolve[{(x^2-1)*y''[x]+4*x*y'[x]+2*y[x]==0,{y[0]==-5,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {5-x}{x^2-1} \\ \end{align*}