83.10.2 problem 2

Internal problem ID [21971]
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 : 2
Date solved : Thursday, October 02, 2025 at 08:20:52 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-4 y^{\prime }+2&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 28

ode:=diff(y(x),x)^2-4*diff(y(x),x)+2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -x \sqrt {2}+c_1 +2 x \\ y &= x \sqrt {2}+c_1 +2 x \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 34

ode=D[y[x],x]^2-4*D[y[x],x]+2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\left (\sqrt {2}-2\right ) x+c_1\\ y(x)&\to \left (2+\sqrt {2}\right ) x+c_1 \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**2 - 4*Derivative(y(x), x) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} - \sqrt {2} x + 2 x, \ y{\left (x \right )} = C_{1} + \sqrt {2} x + 2 x\right ] \]