67.25.5 problem 35.2 (e)

Internal problem ID [17000]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 35. Modified Power series solutions and basic method of Frobenius. Additional Exercises. page 715
Problem number : 35.2 (e)
Date solved : Thursday, October 02, 2025 at 01:41:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 59

Order:=6; 
ode:=3*(x-2)^2*diff(diff(y(x),x),x)-4*(x-5)*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {1}{12} x^{2}+\frac {1}{54} x^{3}+\frac {1}{648} x^{4}-\frac {1}{4860} x^{5}\right ) y \left (0\right )+\left (x -\frac {5}{6} x^{2}+\frac {23}{108} x^{3}+\frac {23}{1296} x^{4}-\frac {23}{9720} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 70

ode=3*(x-2)^2*D[y[x],{x,2}]-4*(x-5)*D[y[x],x]+2*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (-\frac {x^5}{4860}+\frac {x^4}{648}+\frac {x^3}{54}-\frac {x^2}{12}+1\right )+c_2 \left (-\frac {23 x^5}{9720}+\frac {23 x^4}{1296}+\frac {23 x^3}{108}-\frac {5 x^2}{6}+x\right ) \]

✓ Sympy. Time used: 0.357 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*(x - 2)**2*Derivative(y(x), (x, 2)) - (4*x - 20)*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_ordinary",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{2} \left (\frac {x^{4}}{648} + \frac {x^{3}}{54} - \frac {x^{2}}{12} + 1\right ) + C_{1} x \left (\frac {23 x^{3}}{1296} + \frac {23 x^{2}}{108} - \frac {5 x}{6} + 1\right ) + O\left (x^{6}\right ) \]