12.8.6 problem 4

Internal problem ID [1742]
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
Date solved : Monday, January 27, 2025 at 05:34:04 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-5\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.008 (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)
 

\[ y = \frac {-x +5}{x^{2}-1} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 18

DSolve[{(x^2-1)*D[y[x],{x,2}]+4*x*D[y[x],x]+2*y[x]==0,{y[0]==-5,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {5-x}{x^2-1} \]