82.18.24 problem Ex. 26

Internal problem ID [18775]
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. 26
Date solved : Monday, March 31, 2025 at 06:10:30 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

\begin{align*} y&=y^{\prime } x +\frac {m}{y^{\prime }} \end{align*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 53

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

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

✗ Sympy

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

Timed Out