Internal problem ID [1255]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +3\right ) y^{\prime \prime }+\left (1+2 x \right ) y^{\prime }-\left (2-x \right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 1, y^{\prime }\left (-1\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = -1\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 18
Order:=6; dsolve([(3+x)*diff(y(x),x$2)+(1+2*x)*diff(y(x),x)-(2-x)*y(x)=0,y(-1) = 1, D(y)(-1) = 0],y(x),type='series',x=-1);
\[ y \relax (x ) = 1+\frac {3}{4} \left (x +1\right )^{2}-\frac {1}{12} \left (x +1\right )^{3}-\frac {1}{48} \left (x +1\right )^{4}-\frac {1}{120} \left (x +1\right )^{5}+\mathrm {O}\left (\left (x +1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 41
AsymptoticDSolveValue[{(3+x)*y''[x]+(1+2*x)*y'[x]-(2-x)*y[x]==0,{y[-1]==1,y'[-1]==0}},y[x],{x,-1,5}]
\[ y(x)\to -\frac {1}{120} (x+1)^5-\frac {1}{48} (x+1)^4-\frac {1}{12} (x+1)^3+\frac {3}{4} (x+1)^2+1 \]