Internal problem ID [1265]
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: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (7+x \right ) y^{\prime \prime }+\left (8+2 x \right ) y^{\prime }+\left (x +5\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-4\right ) = 1, y^{\prime }\left (-4\right ) = 2] \end {align*}
With the expansion point for the power series method at \(x = -4\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
Order:=6; dsolve([(7+x)*diff(y(x),x$2)+(8+2*x)*diff(y(x),x)+(5+x)*y(x)=0,y(-4) = 1, D(y)(-4) = 2],y(x),type='series',x=-4);
\[ y \relax (x ) = 1+2 \left (x +4\right )-\frac {1}{6} \left (x +4\right )^{2}-\frac {10}{27} \left (x +4\right )^{3}+\frac {19}{648} \left (x +4\right )^{4}+\frac {13}{324} \left (x +4\right )^{5}+\mathrm {O}\left (\left (x +4\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 46
AsymptoticDSolveValue[{(7+x)*y''[x]+(8+2*x)*y'[x]+(5+x)*y[x]==0,{y[-4]==1,y'[-4]==2}},y[x],{x,-4,5}]
\[ y(x)\to \frac {13}{324} (x+4)^5+\frac {19}{648} (x+4)^4-\frac {10}{27} (x+4)^3-\frac {1}{6} (x+4)^2+2 (x+4)+1 \]