Internal problem ID [1259]
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: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (5+2 x \right ) y^{\prime \prime }-y^{\prime }+\left (x +5\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([(5+2*x)*diff(y(x),x$2)-diff(y(x),x)+(5+x)*y(x)=0,y(-2) = 2, D(y)(-2) = -1],y(x),type='series',x=-2);
\[ y \relax (x ) = 2-\left (2+x \right )-\frac {7}{2} \left (2+x \right )^{2}+\frac {4}{3} \left (2+x \right )^{3}-\frac {1}{24} \left (2+x \right )^{4}+\frac {1}{60} \left (2+x \right )^{5}+\mathrm {O}\left (\left (2+x \right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 43
AsymptoticDSolveValue[{(5+2*x)*y''[x]-y'[x]+(5+x)*y[x]==0,{y[-2]==2,y'[-2]==-1}},y[x],{x,-2,5}]
\[ y(x)\to \frac {1}{60} (x+2)^5-\frac {1}{24} (x+2)^4+\frac {4}{3} (x+2)^3-\frac {7}{2} (x+2)^2-x \]