9.7.10 problem problem 10

Internal problem ID [1051]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page 615
Problem number : problem 10
Date solved : Tuesday, March 04, 2025 at 12:08:06 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 37

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

\[ y = \left (1-\frac {3}{2} x +\frac {3}{8} x^{2}+\frac {1}{16} x^{3}+\frac {3}{128} x^{4}+\frac {3}{256} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 41

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

\[ y(x)\to c_1 \left (\frac {3 x^5}{256}+\frac {3 x^4}{128}+\frac {x^3}{16}+\frac {3 x^2}{8}-\frac {3 x}{2}+1\right ) \]

✓ Sympy. Time used: 0.711 (sec). Leaf size: 46

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

\[ y{\left (x \right )} = C_{1} - \frac {3 C_{1} x}{2} + \frac {3 C_{1} x^{2}}{8} + \frac {C_{1} x^{3}}{16} + \frac {3 C_{1} x^{4}}{128} + \frac {3 C_{1} x^{5}}{256} + O\left (x^{6}\right ) \]