63.1.135 problem 194

Internal problem ID [15575]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 194
Date solved : Thursday, October 02, 2025 at 10:20:18 AM
CAS classification : [[_Riccati, _special]]

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

With initial conditions

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

✓ Maple. Time used: 0.204 (sec). Leaf size: 95

ode:=diff(y(x),x) = x+y(x)^2; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (-2 \,3^{{5}/{6}} \pi +3 \Gamma \left (\frac {2}{3}\right )^{2} 3^{{2}/{3}}\right ) \operatorname {AiryAi}\left (1, -x \right )+\left (3 \,3^{{1}/{6}} \Gamma \left (\frac {2}{3}\right )^{2}+2 \pi 3^{{1}/{3}}\right ) \operatorname {AiryBi}\left (1, -x \right )}{\left (-2 \,3^{{5}/{6}} \pi +3 \Gamma \left (\frac {2}{3}\right )^{2} 3^{{2}/{3}}\right ) \operatorname {AiryAi}\left (-x \right )+\left (3 \,3^{{1}/{6}} \Gamma \left (\frac {2}{3}\right )^{2}+2 \pi 3^{{1}/{3}}\right ) \operatorname {AiryBi}\left (-x \right )} \]

✓ Mathematica. Time used: 0.672 (sec). Leaf size: 145

ode=D[y[x],x]==y[x]^2+x; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\sqrt [3]{3} \operatorname {Gamma}\left (\frac {2}{3}\right ) \left (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 )\right )-2 x^{3/2} \operatorname {Gamma}\left (\frac {1}{3}\right ) \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2 x^{3/2}}{3}\right )}{2 x \left (\operatorname {Gamma}\left (\frac {1}{3}\right ) \operatorname {BesselJ}\left (\frac {1}{3},\frac {2 x^{3/2}}{3}\right )-\sqrt [3]{3} \operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )\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): 1} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : bad operand type for unary -: list