23.2.113 problem 115

Internal problem ID [5468]
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 : 115
Date solved : Tuesday, September 30, 2025 at 12:44:02 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

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

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

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

\begin{align*} y &= a -x -2 \sqrt {-a x} \\ y &= a -x +2 \sqrt {-a x} \\ y &= \frac {c_1 \left (c_1 x +a +x \right )}{c_1 +1} \\ \end{align*}

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 60

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

\begin{align*} y(x)&\to c_1 \left (x+\frac {a}{1+c_1}\right )\\ y(x)&\to \left (\sqrt {a}-i \sqrt {x}\right )^2\\ y(x)&\to \left (\sqrt {a}+i \sqrt {x}\right )^2 \end{align*}

✗ Sympy

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

Timed Out