58.1.20 problem 20

Internal problem ID [9091]
Book : Second order enumerated odes
Section : section 1
Problem number : 20
Date solved : Wednesday, March 05, 2025 at 07:19:36 AM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 18

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

\[ y = \ln \left (\pi \right )+\ln \left (c_{1} \operatorname {AiryAi}\left (x \right )-c_{2} \operatorname {AiryBi}\left (x \right )\right ) \]

✓ Mathematica. Time used: 0.202 (sec). Leaf size: 15

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

\[ y(x)\to \log (x-c_1)+c_2 \]

✗ Sympy

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

TypeError : bad operand type for unary -: list