74.18.62 problem 68

Internal problem ID [16548]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 68
Date solved : Monday, March 31, 2025 at 02:56:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+\left (-2 x^{2}+7\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 33

Order:=6; 
ode:=x^2*diff(diff(y(x),x),x)-7*x*diff(y(x),x)+(-2*x^2+7)*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = c_1 \,x^{7} \left (1+\frac {1}{8} x^{2}+\frac {1}{160} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_2 x \left (-86400+21600 x^{2}-5400 x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 44

ode=x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+(7-2*x^2)*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (\frac {x^5}{16}-\frac {x^3}{4}+x\right )+c_2 \left (\frac {x^{11}}{160}+\frac {x^9}{8}+x^7\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 7*x*Derivative(y(x), x) + (7 - 2*x**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

ValueError : Expected Expr or iterable but got None