23.2.129 problem 131

Internal problem ID [5484]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 131
Date solved : Tuesday, September 30, 2025 at 12:45:16 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

\begin{align*} \left (a -x \right ) {y^{\prime }}^{2}+y y^{\prime }-b&=0 \end{align*}

✓ Maple. Time used: 0.095 (sec). Leaf size: 49

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

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

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

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

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

✗ Sympy

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

Timed Out