68.8.36 problem 36

Internal problem ID [17459]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 36
Date solved : Thursday, October 02, 2025 at 02:23:51 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: 0.109 (sec). Leaf size: 30

ode:=diff(y(x),x) = y(x)^2-x; 
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: 7.84 (sec). Leaf size: 93

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

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