Internal problem ID [1223]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN
ORDINARY POINT I. Exercises 7.2. Page 329
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 }-y^{\prime } x -3 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 2] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
Order:=6; dsolve([(x^2-4)*diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=0,y(0) = -1, D(y)(0) = 2],y(x),type='series',x=0);
\[ y \relax (x ) = -1+2 x +\frac {3}{8} x^{2}-\frac {1}{3} x^{3}-\frac {3}{128} x^{4}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 29
AsymptoticDSolveValue[{(x^2-4)*y''[x]-x*y'[x]-3*y[x]==0,{y[0]==-1,y'[0]==2}},y[x],{x,0,5}]
\[ y(x)\to -\frac {3 x^4}{128}-\frac {x^3}{3}+\frac {3 x^2}{8}+2 x-1 \]