67.3.20 problem 4.5 (d)

Internal problem ID [16341]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.5 (d)
Date solved : Thursday, October 02, 2025 at 01:21:09 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y y^{\prime }&=3 \sqrt {x y^{2}+9 x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.269 (sec). Leaf size: 17

ode:=y(x)*diff(y(x),x) = 3*(x*y(x)^2+9*x)^(1/2); 
ic:=[y(1) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 \sqrt {x^{{3}/{2}} \left (x^{{3}/{2}}+3\right )} \]

✓ Mathematica. Time used: 0.207 (sec). Leaf size: 44

ode=y[x]*D[y[x],x]==3*Sqrt[x*y[x]^2+9*x]; 
ic={y[1]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 \sqrt {3 x^{3/2}+x^3}\\ y(x)&\to 2 \sqrt {-7 x^{3/2}+x^3+10} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*sqrt(x*y(x)**2 + 9*x) + y(x)*Derivative(y(x), x),0) 
ics = {y(1): 4} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants