76.1.2 problem 2

Internal problem ID [17230]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 2
Date solved : Monday, March 31, 2025 at 03:45:12 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x^{2} \left (x^{3}+1\right )}{y} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 43

ode:=diff(y(x),x) = x^2/y(x)*(x^3+1); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\sqrt {3 x^{6}+6 x^{3}+9 c_1}}{3} \\ y &= \frac {\sqrt {3 x^{6}+6 x^{3}+9 c_1}}{3} \\ \end{align*}

✓ Mathematica. Time used: 0.138 (sec). Leaf size: 56

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

\begin{align*} y(x)\to -\frac {\sqrt {x^6+2 x^3+6 c_1}}{\sqrt {3}} \\ y(x)\to \frac {\sqrt {x^6+2 x^3+6 c_1}}{\sqrt {3}} \\ \end{align*}

✓ Sympy. Time used: 0.380 (sec). Leaf size: 39

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} + 3 x^{6} + 6 x^{3}}}{3}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} + 3 x^{6} + 6 x^{3}}}{3}\right ] \]