87.23.1 problem 15

Internal problem ID [23782]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 5. Series solutions of second order linear equations. Exercise at page 215
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:45:07 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 y \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 37

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

\[ y = \left (1+3 x +\frac {9}{2} x^{2}+\frac {9}{2} x^{3}+\frac {27}{8} x^{4}+\frac {81}{40} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 39

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

\[ y(x)\to c_1 \left (\frac {81 x^5}{40}+\frac {27 x^4}{8}+\frac {9 x^3}{2}+\frac {9 x^2}{2}+3 x+1\right ) \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 46

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

\[ y{\left (x \right )} = C_{1} + 3 C_{1} x + \frac {9 C_{1} x^{2}}{2} + \frac {9 C_{1} x^{3}}{2} + \frac {27 C_{1} x^{4}}{8} + \frac {81 C_{1} x^{5}}{40} + O\left (x^{6}\right ) \]