58.4.17 problem 17

Internal problem ID [14587]
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 : 17
Date solved : Thursday, October 02, 2025 at 09:43:13 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.088 (sec). Leaf size: 21

ode:=(3*x+8)*(y(x)^2+4)-4*y(x)*(x^2+5*x+6)*diff(y(x),x) = 0; 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 4.063 (sec). Leaf size: 36

ode=(3*x+8)*(y[x]^2+4)-4*y[x]*(x^2+5*x+6)*D[y[x],x]==0; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3*x + 8)*(y(x)**2 + 4) - (4*x**2 + 20*x + 24)*y(x)*Derivative(y(x), x),0) 
ics = {y(1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants