23.2.111 problem 113

Internal problem ID [5466]
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 : 113
Date solved : Tuesday, September 30, 2025 at 12:44:01 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.082 (sec). Leaf size: 42

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 58

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

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

✗ Sympy

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

Timed Out