82.18.2 problem Ex. 2

Internal problem ID [18753]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Examples on chapter III. page 38
Problem number : Ex. 2
Date solved : Monday, March 31, 2025 at 06:07:50 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.046 (sec). Leaf size: 49

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

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 59

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

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

✗ Sympy

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

Timed Out