85.13.3 problem 3

Internal problem ID [22509]
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. B Exercises at page 40
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:44:01 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y^{\prime }&=\frac {6 x^{2}-5 y x -2 y^{2}}{6 x^{2}-8 y x +y^{2}} \end{align*}

✓ Maple. Time used: 0.181 (sec). Leaf size: 154

ode:=diff(y(x),x) = (6*x^2-5*x*y(x)-2*y(x)^2)/(6*x^2-8*x*y(x)+y(x)^2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (x^{2} c_1 \,\textit {\_Z}^{24}-12 x^{2} c_1 \,\textit {\_Z}^{22}+\left (66 c_1 \,x^{2}-1\right ) \textit {\_Z}^{20}+\left (-220 c_1 \,x^{2}+18\right ) \textit {\_Z}^{18}+\left (495 c_1 \,x^{2}-144\right ) \textit {\_Z}^{16}+\left (-792 c_1 \,x^{2}+672\right ) \textit {\_Z}^{14}+\left (924 c_1 \,x^{2}-2016\right ) \textit {\_Z}^{12}+\left (-792 c_1 \,x^{2}+4032\right ) \textit {\_Z}^{10}+\left (495 c_1 \,x^{2}-5376\right ) \textit {\_Z}^{8}+\left (-220 c_1 \,x^{2}+4608\right ) \textit {\_Z}^{6}+\left (66 c_1 \,x^{2}-2304\right ) \textit {\_Z}^{4}+\left (-12 c_1 \,x^{2}+512\right ) \textit {\_Z}^{2}+c_1 \,x^{2}\right )^{2} x +x \]

✓ Mathematica. Time used: 60.12 (sec). Leaf size: 2977

ode=D[y[x],x]==(6*x^2-5*x*y[x]-2*y[x]^2)/(6*x^2-8*x*y[x]+y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 0.873 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (6*x**2 - 5*x*y(x) - 2*y(x)**2)/(6*x**2 - 8*x*y(x) + y(x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (x \right )} = C_{1} + \log {\left (\frac {\left (-3 + \frac {y{\left (x \right )}}{x}\right )^{\frac {9}{2}} \sqrt {-1 + \frac {y{\left (x \right )}}{x}}}{\left (-2 + \frac {y{\left (x \right )}}{x}\right )^{6}} \right )} \]