23.1.679 problem 674

Internal problem ID [5286]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 674
Date solved : Tuesday, September 30, 2025 at 12:07:20 PM
CAS classification : [_exact, _rational]

\begin{align*} x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 735

ode:=x*(3+5*x-12*x*y(x)^2+4*x^2*y(x))*diff(y(x),x)+(3+10*x-8*x*y(x)^2+6*x^2*y(x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 60.123 (sec). Leaf size: 660

ode=x(3+5 x-12 x y[x]^2+4 x^2 y[x])D[y[x],x]+(3+10 x-8 x y[x]^2+6 x^2 y[x])y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt [3]{-16 x^9-360 x^7-216 x^6+432 c_1 x^4+8 \sqrt {-4 x^9 \left (x^3+15 x+9\right )^3+\left (2 x^9+45 x^7+27 x^6-54 c_1 x^4\right ){}^2}}}{12 \sqrt [3]{2} x^2}-\frac {\left (x^3+15 x+9\right ) x}{3\ 2^{2/3} \sqrt [3]{-2 x^9-45 x^7-27 x^6+54 c_1 x^4+3 \sqrt {3} \sqrt {-x^8 \left (25 x^6+(30+8 c_1) x^5+509 x^4+180 (5+c_1) x^3+108 (5+c_1) x^2+108 x-108 c_1{}^2\right )}}}+\frac {x}{6}\\ y(x)&\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-16 x^9-360 x^7-216 x^6+432 c_1 x^4+8 \sqrt {-4 x^9 \left (x^3+15 x+9\right )^3+\left (2 x^9+45 x^7+27 x^6-54 c_1 x^4\right ){}^2}}}{24 \sqrt [3]{2} x^2}+\frac {\left (1+i \sqrt {3}\right ) \left (x^3+15 x+9\right ) x}{6\ 2^{2/3} \sqrt [3]{-2 x^9-45 x^7-27 x^6+54 c_1 x^4+3 \sqrt {3} \sqrt {-x^8 \left (25 x^6+(30+8 c_1) x^5+509 x^4+180 (5+c_1) x^3+108 (5+c_1) x^2+108 x-108 c_1{}^2\right )}}}+\frac {x}{6}\\ y(x)&\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-16 x^9-360 x^7-216 x^6+432 c_1 x^4+8 \sqrt {-4 x^9 \left (x^3+15 x+9\right )^3+\left (2 x^9+45 x^7+27 x^6-54 c_1 x^4\right ){}^2}}}{24 \sqrt [3]{2} x^2}+\frac {\left (1-i \sqrt {3}\right ) \left (x^3+15 x+9\right ) x}{6\ 2^{2/3} \sqrt [3]{-2 x^9-45 x^7-27 x^6+54 c_1 x^4+3 \sqrt {3} \sqrt {-x^8 \left (25 x^6+(30+8 c_1) x^5+509 x^4+180 (5+c_1) x^3+108 (5+c_1) x^2+108 x-108 c_1{}^2\right )}}}+\frac {x}{6} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(4*x**2*y(x) - 12*x*y(x)**2 + 5*x + 3)*Derivative(y(x), x) + (6*x**2*y(x) - 8*x*y(x)**2 + 10*x + 3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out