87.15.18 problem 18

Internal problem ID [23566]
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 2. Linear differential equations. Exercise at page 115
Problem number : 18
Date solved : Thursday, October 02, 2025 at 09:42:59 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+3 y x&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.160 (sec). Leaf size: 24

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

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