7.7.9 problem 9

Internal problem ID [187]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 9
Date solved : Saturday, March 29, 2025 at 04:38:50 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

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

ode:=x*diff(y(x),x)+2*y(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: 0.158 (sec). Leaf size: 17

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

\[ y(x)\to \frac {\left (x^3+c_1\right ){}^2}{x^2} \]

✓ Sympy. Time used: 0.246 (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)
 

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