Internal problem ID [1217]
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: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {\left (8 x^{2}+1\right ) y^{\prime \prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = -1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(1+8*x^2)*diff(y(x),x$2)+2*y(x)=0,y(0) = 2, D(y)(0) = -1],y(x),type='series',x=0);
\[ y \relax (x ) = 2-x -2 x^{2}+\frac {1}{3} x^{3}+3 x^{4}-\frac {5}{6} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 32
AsymptoticDSolveValue[{(1+8*x^2)*y''[x]+2*y[x]==0,{y[0]==2,y'[0]==-1}},y[x],{x,0,5}]
\[ y(x)\to -\frac {5 x^5}{6}+3 x^4+\frac {x^3}{3}-2 x^2-x+2 \]