26.6.6 problem Exercise 12.6, page 103

Internal problem ID [7006]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.6, page 103
Date solved : Tuesday, September 30, 2025 at 04:14:07 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} \left (x -y\right )^{2} y^{\prime }&=4 \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 27

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

\[ y-\ln \left (-x +y+2\right )+\ln \left (-x +y-2\right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.148 (sec). Leaf size: 99

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

\[ \text {Solve}\left [\int _1^x\left (\frac {1}{K[1]-y(x)+2}-\frac {1}{K[1]-y(x)-2}\right )dK[1]+\int _1^{y(x)}\left (-\int _1^x\left (\frac {1}{(K[1]-K[2]+2)^2}-\frac {1}{(K[1]-K[2]-2)^2}\right )dK[1]+\frac {1}{-x+K[2]-2}-\frac {1}{-x+K[2]+2}+1\right )dK[2]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.694 (sec). Leaf size: 22

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

\[ C_{1} + y{\left (x \right )} - \log {\left (x - y{\left (x \right )} - 2 \right )} + \log {\left (x - y{\left (x \right )} + 2 \right )} = 0 \]