84.5.4 problem 3.1 (d)

Internal problem ID [22091]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Solved problems. Page 11
Problem number : 3.1 (d)
Date solved : Thursday, October 02, 2025 at 08:23:51 PM
CAS classification : [[_Riccati, _special]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 31

ode:=diff(y(x),x) = x+y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \operatorname {AiryAi}\left (1, -x \right )+\operatorname {AiryBi}\left (1, -x \right )}{c_1 \operatorname {AiryAi}\left (-x \right )+\operatorname {AiryBi}\left (-x \right )} \]

✓ Mathematica. Time used: 0.079 (sec). Leaf size: 195

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

\begin{align*} y(x)&\to \frac {x^{3/2} \left (-2 \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2 x^{3/2}}{3}\right )+c_1 \left (\operatorname {BesselJ}\left (\frac {2}{3},\frac {2 x^{3/2}}{3}\right )-\operatorname {BesselJ}\left (-\frac {4}{3},\frac {2 x^{3/2}}{3}\right )\right )\right )-c_1 \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )}{2 x \left (\operatorname {BesselJ}\left (\frac {1}{3},\frac {2 x^{3/2}}{3}\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )\right )}\\ 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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : bad operand type for unary -: list