58.4.20 problem 20

Internal problem ID [14590]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 20
Date solved : Thursday, October 02, 2025 at 09:43:25 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 x^{2}+9 y x +5 y^{2}-\left (6 x^{2}+4 y x \right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=-6 \\ \end{align*}

✓ Maple. Time used: 0.120 (sec). Leaf size: 21

ode:=3*x^2+9*x*y(x)+5*y(x)^2-(6*x^2+4*x*y(x))*diff(y(x),x) = 0; 
ic:=[y(2) = -6]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {\left (3+\sqrt {-3+6 \sqrt {2}\, \sqrt {x}}\right ) x}{2} \]

✓ Mathematica. Time used: 20.198 (sec). Leaf size: 30

ode=(3*x^2+9*x*y[x]+5*y[x]^2)-(6*x^2+4*x*y[x])*D[y[x],x]==0; 
ic={y[2]==-6}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{2} \left (\sqrt {6 \sqrt {2} \sqrt {x}-3}+3\right ) x \end{align*}

✓ Sympy. Time used: 1.797 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2 + 9*x*y(x) - (6*x**2 + 4*x*y(x))*Derivative(y(x), x) + 5*y(x)**2,0) 
ics = {y(2): -6} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x \left (- \sqrt {6 \sqrt {2} \sqrt {x} - 3} - 3\right )}{2} \]