56.17.2 problem Ex 2

Internal problem ID [14183]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
Problem number : Ex 2
Date solved : Thursday, October 02, 2025 at 09:25:14 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.096 (sec). Leaf size: 49

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

\begin{align*} y &= -2 \sqrt {-a \left (b -x \right )} \\ y &= 2 \sqrt {-a \left (b -x \right )} \\ y &= \frac {\left (x -b \right ) c_1^{2}+a}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 59

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

\begin{align*} y(x)&\to \frac {a}{c_1}+c_1 (x-b)\\ y(x)&\to \text {Indeterminate}\\ y(x)&\to -2 \sqrt {a (x-b)}\\ y(x)&\to 2 \sqrt {a (x-b)} \end{align*}

✗ Sympy

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

Timed Out