60.1.418 problem 429

Internal problem ID [10432]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 429
Date solved : Sunday, March 30, 2025 at 04:41:50 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

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

✓ Maple. Time used: 0.169 (sec). Leaf size: 72

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 90

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

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

✗ Sympy

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

Timed Out