82.12.16 problem Ex. 16

Internal problem ID [18710]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 16
Date solved : Monday, March 31, 2025 at 06:02:08 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.192 (sec). Leaf size: 25

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

\[ y = \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} m +\ln \left (x^{2} \sec \left (\textit {\_Z} \right )^{2}\right )+2 c_1 \right )\right ) x \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 34

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

\[ \text {Solve}\left [m \arctan \left (\frac {y(x)}{x}\right )-\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out