2.6.9 problem 9

Internal problem ID [779]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 04:11:19 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2 y+x y^{\prime }&=6 x^{2} \sqrt {y} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

ode:=2*y(x)+x*diff(y(x),x) = 6*x^2*y(x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {-x^{3}+\sqrt {y}\, x -c_1}{x} = 0 \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to \frac {\left (x^3+c_1\right ){}^2}{x^2} \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 17

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

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