Internal problem ID [1286]
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: 44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (3 x^{2}+12 x +13\right ) y^{\prime }+\left (5+2 x \right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-2\right ) = 2, y^{\prime }\left (-2\right ) = -3] \end {align*}
With the expansion point for the power series method at \(x = -2\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(x),x$2)+(13+12*x+3*x^2)*diff(y(x),x)+(5+2*x)*y(x)=0,y(-2) = 2, D(y)(-2) = -3],y(x),type='series',x=-2);
\[ y \relax (x ) = 2-3 \left (2+x \right )+\frac {1}{2} \left (2+x \right )^{2}-\frac {1}{3} \left (2+x \right )^{3}+\frac {31}{24} \left (2+x \right )^{4}-\frac {53}{120} \left (2+x \right )^{5}+\mathrm {O}\left (\left (2+x \right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 46
AsymptoticDSolveValue[{y''[x]+(13+12*x+3*x^2)*y'[x]+(5+2*x)*y[x]==0,{y[-2]==2,y'[-2]==-3}},y[x],{x,-2,5}]
\[ y(x)\to -\frac {53}{120} (x+2)^5+\frac {31}{24} (x+2)^4-\frac {1}{3} (x+2)^3+\frac {1}{2} (x+2)^2-3 (x+2)+2 \]