23.2.115 problem 117

Internal problem ID [5470]
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 : 117
Date solved : Tuesday, September 30, 2025 at 12:44:10 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

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

✓ Maple. Time used: 0.038 (sec). Leaf size: 55

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

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 70

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

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

✗ Sympy

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

Timed Out