Internal problem ID [1250]
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: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 1, y^{\prime }\left (-1\right ) = -1] \end {align*}
With the expansion point for the power series method at \(x = -1\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(3*x+2*x^2)*diff(y(x),x$2)+10*(1+x)*diff(y(x),x)+8*y(x)=0,y(-1) = 1, D(y)(-1) = -1],y(x),type='series',x=-1);
\[ y \relax (x ) = 1-\left (x +1\right )+4 \left (x +1\right )^{2}-\frac {13}{3} \left (x +1\right )^{3}+\frac {77}{6} \left (x +1\right )^{4}-\frac {278}{15} \left (x +1\right )^{5}+\mathrm {O}\left (\left (x +1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 41
AsymptoticDSolveValue[{(3*x+2*x^2)*y''[x]+10*(1+x)*y'[x]+8*y[x]==0,{y[-1]==1,y'[-1]==-1}},y[x],{x,-1,5}]
\[ y(x)\to -\frac {278}{15} (x+1)^5+\frac {77}{6} (x+1)^4-\frac {13}{3} (x+1)^3+4 (x+1)^2-x \]