75.23.1 problem 724

Internal problem ID [17119]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 18.1 Integration of differential equation in series. Power series. Exercises page 171
Problem number : 724
Date solved : Thursday, March 13, 2025 at 09:16:33 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=1-x y \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 14

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

\[ y = x -\frac {1}{3} x^{3}+\frac {1}{15} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 19

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

\[ y(x)\to \frac {x^5}{15}-\frac {x^3}{3}+x \]

✓ Sympy. Time used: 0.646 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = x - \frac {x^{3}}{3} + \frac {x^{5}}{15} + O\left (x^{6}\right ) \]