Internal problem ID [1269]
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: 31(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (6 x^{2}-5 x +1\right ) y^{\prime \prime }-\left (10-24 x \right ) y^{\prime }+12 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
Order:=6; dsolve((1-5*x+6*x^2)*diff(y(x),x$2)-(10-24*x)*diff(y(x),x)+12*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (-390 x^{5}-114 x^{4}-30 x^{3}-6 x^{2}+1\right ) y \relax (0)+\left (211 x^{5}+65 x^{4}+19 x^{3}+5 x^{2}+x \right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 54
AsymptoticDSolveValue[(1-5*x+6*x^2)*y''[x]-(10-24*x)*y'[x]+12*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-390 x^5-114 x^4-30 x^3-6 x^2+1\right )+c_2 \left (211 x^5+65 x^4+19 x^3+5 x^2+x\right ) \]