85.14.6 problem 5 (a)

Internal problem ID [22522]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. C Exercises at page 41
Problem number : 5 (a)
Date solved : Thursday, October 02, 2025 at 08:45:31 PM
CAS classification : [[_homogeneous, `class C`], _rational]

\begin{align*} y^{\prime }&=\frac {\left (x -3 y-5\right )^{2}}{\left (x +y-1\right )^{2}} \end{align*}

✓ Maple. Time used: 0.285 (sec). Leaf size: 79

ode:=diff(y(x),x) = (x-3*y(x)-5)^2/(x+y(x)-1)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \ln \left (\frac {-3-y+x}{x -2}\right )-\ln \left (\frac {y^{2}+\left (-6 x +14\right ) y+x^{2}-10 x +17}{\left (x -2\right )^{2}}\right )+\sqrt {2}\, \operatorname {arctanh}\left (\frac {\left (7+y-3 x \right ) \sqrt {2}}{4 x -8}\right )-\ln \left (x -2\right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.138 (sec). Leaf size: 88

ode=D[y[x],x]==  ( (x-3*y[x]-5)/(x+y[x]-1))^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{2} \left (-2 \log (-y(x)+x-3)+\left (2+\sqrt {2}\right ) \log \left (2 \sqrt {2} y(x)-3 y(x)+x+2 \sqrt {2}-5\right )-\left (\sqrt {2}-2\right ) \log \left (2 \sqrt {2} y(x)+3 y(x)-x+2 \sqrt {2}+5\right )\right )=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x - 3*y(x) - 5)**2/(x + y(x) - 1)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out