64.7.5 problem 5

Internal problem ID [13308]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page 67
Problem number : 5
Date solved : Monday, March 31, 2025 at 07:50:33 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 23

ode:=4*x*y(x)^2+6*y(x)+(5*x^2*y(x)+8*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_1 +\ln \left (2+\textit {\_Z} \right )+4 \ln \left (\textit {\_Z} \right )\right )}{x} \]

✓ Mathematica. Time used: 0.203 (sec). Leaf size: 64

ode=(4*x*y[x]^2+6*y[x])+(5*x^2*y[x]+8*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [6^{2/3} \log (x)+20 c_1=20 \int _1^{\frac {5 x y(x)+16}{\sqrt [3]{6} (5 x y(x)+8)}}\frac {1}{K[1]^3-\frac {7 K[1]}{6^{2/3}}+1}dK[1],y(x)\right ] \]

✓ Sympy. Time used: 0.528 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*y(x)**2 + (5*x**2*y(x) + 8*x)*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - \log {\left (x \right )} + 4 \log {\left (x y{\left (x \right )} \right )} + \log {\left (x y{\left (x \right )} + 2 \right )} = C_{1} \]