Internal problem ID [1288]
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: 46.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+4 x +3\right ) y^{\prime \prime }-\left (-x^{2}+4 x +5\right ) y^{\prime }-\left (2+x \right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-2\right ) = 2, y^{\prime }\left (-2\right ) = -1] \end {align*}
With the expansion point for the power series method at \(x = -2\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([(3+4*x+x^2)*diff(y(x),x$2)-(5+4*x-x^2)*diff(y(x),x)-(2+x)*y(x)=0,y(-2) = 2, D(y)(-2) = -1],y(x),type='series',x=-2);
\[ y \relax (x ) = 2-\left (2+x \right )-\frac {7}{2} \left (2+x \right )^{2}-\frac {43}{6} \left (2+x \right )^{3}-\frac {203}{24} \left (2+x \right )^{4}-\frac {167}{30} \left (2+x \right )^{5}+\mathrm {O}\left (\left (2+x \right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 43
AsymptoticDSolveValue[{(3+4*x+x^2)*y''[x]-(5+4*x-x^2)*y'[x]-(2+x)*y[x]==0,{y[-2]==2,y'[-2]==-1}},y[x],{x,-2,5}]
\[ y(x)\to -\frac {167}{30} (x+2)^5-\frac {203}{24} (x+2)^4-\frac {43}{6} (x+2)^3-\frac {7}{2} (x+2)^2-x \]