12.13.28 problem 31(b)

Internal problem ID [1919]
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)
Date solved : Monday, January 27, 2025 at 05:38:24 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (6 x^{2}-5 x +1\right ) y^{\prime \prime }-\left (10-24 x \right ) y^{\prime }+12 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 59

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);
 

\[ y = \left (-390 x^{5}-114 x^{4}-30 x^{3}-6 x^{2}+1\right ) y \left (0\right )+\left (211 x^{5}+65 x^{4}+19 x^{3}+5 x^{2}+x \right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 54

AsymptoticDSolveValue[(1-5*x+6*x^2)*D[y[x],{x,2}]-(10-24*x)*D[y[x],x]+12*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (-390 x^5-114 x^4-30 x^3-6 x^2+1\right )+c_2 \left (211 x^5+65 x^4+19 x^3+5 x^2+x\right ) \]