79.7.2 problem (b.1)

Internal problem ID [21103]
Book : Ordinary Differential Equations. By Wolfgang Walter. Graduate texts in Mathematics. Springer. NY. QA372.W224 1998
Section : Chapter 2. Theory of First order differential equations. Excercises IV at page 89
Problem number : (b.1)
Date solved : Thursday, October 02, 2025 at 07:08:22 PM
CAS classification : [_Abel]

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

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

Order:=6; 
ode:=diff(y(x),x) = x^3+y(x)^3; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x),type='series',x=0);
 

\[ y = 1+x +\frac {3}{2} x^{2}+\frac {5}{2} x^{3}+\frac {37}{8} x^{4}+\frac {321}{40} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 34

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

\[ y(x)\to \frac {321 x^5}{40}+\frac {37 x^4}{8}+\frac {5 x^3}{2}+\frac {3 x^2}{2}+x+1 \]

✓ Sympy. Time used: 0.193 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = 1 + x + \frac {3 x^{2}}{2} + \frac {5 x^{3}}{2} + \frac {37 x^{4}}{8} + \frac {321 x^{5}}{40} + O\left (x^{6}\right ) \]