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 : Tuesday, March 04, 2025 at 01:46:13 PM
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*}

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

Order:=6; 
ode:=(6*x^2-5*x+1)*diff(diff(y(x),x),x)-(10-24*x)*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

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

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

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

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

✓ Sympy. Time used: 0.823 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((24*x - 10)*Derivative(y(x), x) + (6*x**2 - 5*x + 1)*Derivative(y(x), (x, 2)) + 12*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_ordinary",x0=0,n=6)
 

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