Internal problem ID [1243]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.3 SERIES SOLUTIONS NEAR AN
ORDINARY POINT II. Exercises 7.3. Page 338
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+8 x \right ) y^{\prime }+4 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: 0.002 (sec). Leaf size: 18
Order:=6; dsolve([(1+x+2*x^2)*diff(y(x),x$2)+(2+8*x)*diff(y(x),x)+4*y(x)=0,y(0) = -1, D(y)(0) = 2],y(x),type='series',x=0);
\[ y \relax (x ) = -1+2 x -4 x^{3}+4 x^{4}+4 x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 23
AsymptoticDSolveValue[{(1+x+2*x^2)*y''[x]+(2+8*x)*y'[x]+4*y[x]==0,{y[0]==-1,y'[0]==2}},y[x],{x,0,5}]
\[ y(x)\to 4 x^5+4 x^4-4 x^3+2 x-1 \]