88.25.14 problem 12

Internal problem ID [24219]
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 : 12
Date solved : Thursday, October 02, 2025 at 10:00:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-3 x y^{\prime }+\left (3-2 x \right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 45

Order:=6; 
ode:=x^2*(1+x)*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+(3-2*x)*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = c_1 \,x^{3} \left (1-\frac {4}{3} x +\frac {5}{3} x^{2}-2 x^{3}+\frac {7}{3} x^{4}-\frac {8}{3} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_2 x \left (-2+4 x -6 x^{2}+8 x^{3}-10 x^{4}+12 x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 62

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

\[ y(x)\to c_1 \left (5 x^5-4 x^4+3 x^3-2 x^2+x\right )+c_2 \left (\frac {7 x^7}{3}-2 x^6+\frac {5 x^5}{3}-\frac {4 x^4}{3}+x^3\right ) \]

✓ Sympy. Time used: 0.365 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(x + 1)*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) + (3 - 2*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{2} x^{3} + C_{1} x + O\left (x^{6}\right ) \]