73.2.5 problem 3.4 e

Internal problem ID [14957]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 3. Some basics about First order equations. Additional exercises. page 63
Problem number : 3.4 e
Date solved : Monday, March 31, 2025 at 01:08:49 PM
CAS classification : [[_Riccati, _special]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 31

ode:=diff(y(x),x)-y(x)^2 = x; 
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: 0.116 (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