Internal problem ID [1260]
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: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +4\right ) y^{\prime \prime }-\left (2 x +4\right ) y^{\prime }+\left (x +6\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-3\right ) = 2, y^{\prime }\left (-3\right ) = -2] \end {align*}
With the expansion point for the power series method at \(x = -3\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(4+x)*diff(y(x),x$2)-(4+2*x)*diff(y(x),x)+(6+x)*y(x)=0,y(-3) = 2, D(y)(-3) = -2],y(x),type='series',x=-3);
\[ y \relax (x ) = 2-2 \left (x +3\right )-\left (x +3\right )^{2}+\left (x +3\right )^{3}-\frac {11}{12} \left (x +3\right )^{4}+\frac {67}{60} \left (x +3\right )^{5}+\mathrm {O}\left (\left (x +3\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 40
AsymptoticDSolveValue[{(4+x)*y''[x]-(4+2*x)*y'[x]+(6+x)*y[x]==0,{y[-3]==2,y'[-3]==-2}},y[x],{x,-3,5}]
\[ y(x)\to \frac {67}{60} (x+3)^5-\frac {11}{12} (x+3)^4+(x+3)^3-(x+3)^2-2 (x+3)+2 \]