15.25.10 problem 9

Internal problem ID [3397]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 43, page 209
Problem number : 9
Date solved : Sunday, March 30, 2025 at 01:39:07 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y&=x -1 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 47

Order:=6; 
ode:=9*x^2*diff(diff(y(x),x),x)+10*x*diff(y(x),x)+y(x) = x-1; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = c_1 \,x^{-\frac {1}{18}-\frac {i \sqrt {35}}{18}} \left (1+\operatorname {O}\left (x^{6}\right )\right )+c_2 \,x^{-\frac {1}{18}+\frac {i \sqrt {35}}{18}} \left (1+\operatorname {O}\left (x^{6}\right )\right )+\left (-1+\frac {1}{11} x +\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.382 (sec). Leaf size: 198

ode=9*x^2*D[y[x],{x,2}]+10*x*D[y[x],x]+y[x]==x-1; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to \frac {9 i \left (\left (\sqrt {35}-i\right ) x-\sqrt {35}+19 i\right ) x^{\frac {1}{18} \left (-1-i \sqrt {35}\right )+\frac {1}{18} \left (1+i \sqrt {35}\right )}}{\sqrt {35} \left (10 \sqrt {35}+8 i\right )}-\frac {9 i \left (\left (\sqrt {35}+i\right ) x-\sqrt {35}-19 i\right ) x^{\frac {1}{18} \left (1-i \sqrt {35}\right )+\frac {1}{18} \left (-1+i \sqrt {35}\right )}}{\sqrt {35} \left (10 \sqrt {35}-8 i\right )}+c_2 x^{\frac {1}{18} \left (-1+i \sqrt {35}\right )}+c_1 x^{\frac {1}{18} \left (-1-i \sqrt {35}\right )} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2*Derivative(y(x), (x, 2)) + 10*x*Derivative(y(x), x) - x + y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

ValueError : ODE 9*x**2*Derivative(y(x), (x, 2)) + 10*x*Derivative(y(x), x) - x + y(x) + 1 does not match hint 2nd_power_series_regular