Internal problem ID [1225]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+12 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -1, y^{\prime }\relax (1) = 1] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 20
Order:=6; dsolve([(5-6*x+3*x^2)*diff(y(x),x$2)+(x-1)*diff(y(x),x)+12*y(x)=0,y(1) = -1, D(y)(1) = 1],y(x),type='series',x=1);
\[ y \relax (x ) = -1+\left (x -1\right )+3 \left (x -1\right )^{2}-\frac {13}{12} \left (x -1\right )^{3}-\frac {5}{2} \left (x -1\right )^{4}+\frac {143}{160} \left (x -1\right )^{5}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 40
AsymptoticDSolveValue[{(5-6*x+3*x^2)*y''[x]+(x-1)*y'[x]+12*y[x]==0,{y[1]==-1,y'[1]==1}},y[x],{x,1,5}]
\[ y(x)\to \frac {143}{160} (x-1)^5-\frac {5}{2} (x-1)^4-\frac {13}{12} (x-1)^3+3 (x-1)^2+x-2 \]