83.10.17 problem 17

Internal problem ID [21986]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter IV. First order differential equations of higher degree. Ex. XI at page 69
Problem number : 17
Date solved : Thursday, October 02, 2025 at 08:21:25 PM
CAS classification : [_quadrature]

\begin{align*} x -{y^{\prime }}^{2} x&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=x-x*diff(y(x),x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= x +c_1 \\ y &= -x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to -x+c_1\\ y(x)&\to x+c_1 \end{align*}

✓ Sympy. Time used: 0.074 (sec). Leaf size: 10

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

\[ \left [ y{\left (x \right )} = C_{1} - x, \ y{\left (x \right )} = C_{1} + x\right ] \]