Internal problem ID [1228]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN
ORDINARY POINT I. Exercises 7.2. Page 329
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 3, y^{\prime }\left (-1\right ) = -3] \end {align*}
With the expansion point for the power series method at \(x = -1\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(2*x^2+4*x+5)*diff(y(x),x$2)-20*(x+1)*diff(y(x),x)+60*y(x)=0,y(-1) = 3, D(y)(-1) = -3],y(x),type='series',x=-1);
\[ y \relax (x ) = 3-3 \left (x +1\right )-30 \left (x +1\right )^{2}+\frac {20}{3} \left (x +1\right )^{3}+20 \left (x +1\right )^{4}-\frac {4}{3} \left (x +1\right )^{5}+\mathrm {O}\left (\left (x +1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[{(2*x^2+4*x+5)*y''[x]-20*(x+1)*y'[x]+60*y[x]==0,{y[-1]==3,y'[-1]==-3}},y[x],{x,-1,5}]
\[ y(x)\to -\frac {4}{3} (x+1)^5+20 (x+1)^4+\frac {20}{3} (x+1)^3-30 (x+1)^2-3 (x+1)+3 \]