Internal problem ID [1226]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {\left (4 x^{2}-24 x +37\right ) y^{\prime \prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (3) = 4, y^{\prime }\relax (3) = -6] \end {align*}
With the expansion point for the power series method at \(x = 3\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(4*x^2-24*x+37)*diff(y(x),x$2)+y(x)=0,y(3) = 4, D(y)(3) = -6],y(x),type='series',x=3);
\[ y \relax (x ) = 4-6 \left (x -3\right )-2 \left (x -3\right )^{2}+\left (x -3\right )^{3}+\frac {3}{2} \left (x -3\right )^{4}-\frac {5}{4} \left (x -3\right )^{5}+\mathrm {O}\left (\left (x -3\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 40
AsymptoticDSolveValue[{(4*x^2-24*x+37)*y''[x]+y[x]==0,{y[3]==4,y'[3]==-6}},y[x],{x,3,5}]
\[ y(x)\to -\frac {5}{4} (x-3)^5+\frac {3}{2} (x-3)^4+(x-3)^3-2 (x-3)^2-6 (x-3)+4 \]