89.4.26 problem 27

Internal problem ID [24348]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 39
Problem number : 27
Date solved : Thursday, October 02, 2025 at 10:20:55 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=2*x^5*diff(y(x),x) = y(x)*(3*x^4+y(x)^2); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {x^{2}}{\sqrt {c_1 x +1}} \\ y &= -\frac {x^{2}}{\sqrt {c_1 x +1}} \\ \end{align*}

✓ Mathematica. Time used: 0.148 (sec). Leaf size: 43

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

\begin{align*} y(x)&\to -\frac {x^2}{\sqrt {1+c_1 x}}\\ y(x)&\to \frac {x^2}{\sqrt {1+c_1 x}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.478 (sec). Leaf size: 32

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

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