69.3.2 problem 42

Internal problem ID [17986]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 3. The method of successive approximation. Exercises page 31
Problem number : 42
Date solved : Thursday, October 02, 2025 at 02:32:05 PM
CAS classification : [[_Riccati, _special]]

\begin{align*} y^{\prime }&=x +y^{2} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.104 (sec). Leaf size: 35

ode:=diff(y(x),x) = x+y(x)^2; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\sqrt {3}\, \operatorname {AiryAi}\left (1, -x \right )+\operatorname {AiryBi}\left (1, -x \right )}{\sqrt {3}\, \operatorname {AiryAi}\left (-x \right )+\operatorname {AiryBi}\left (-x \right )} \]

✓ Mathematica. Time used: 0.775 (sec). Leaf size: 80

ode=D[y[x],x]==x+y[x]^2; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^{3/2} \operatorname {BesselJ}\left (-\frac {4}{3},\frac {2 x^{3/2}}{3}\right )-x^{3/2} \operatorname {BesselJ}\left (\frac {2}{3},\frac {2 x^{3/2}}{3}\right )+\operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )}{2 x \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - y(x)**2 + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : bad operand type for unary -: list