88.25.12 problem 10

Internal problem ID [24217]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 7. Series Methods. Exercises at page 212
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:00:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-\left (3 x^{4}+5 x \right ) y^{\prime }+\left (6 x^{3}+5\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 29

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

\[ y = c_1 \,x^{5} \left (1+\frac {3}{7} x^{3}+\operatorname {O}\left (x^{6}\right )\right )+c_2 x \left (-144-144 x^{3}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 26

ode=x^2*D[y[x],{x,2}]-(5*x+3*x^4)*D[y[x],{x,1}]+(5+6*x^3)*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + (6*x**3 + 5)*y(x) - (3*x**4 + 5*x)*Derivative(y(x), 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