64.5.16 problem 16

Internal problem ID [13258]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 16
Date solved : Monday, March 31, 2025 at 07:43:55 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+y&=-2 x^{6} y^{4} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 65

ode:=x*diff(y(x),x)+y(x) = -2*x^6*y(x)^4; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{\left (2 x^{3}+c_1 \right )^{{1}/{3}} x} \\ y &= -\frac {1+i \sqrt {3}}{2 \left (2 x^{3}+c_1 \right )^{{1}/{3}} x} \\ y &= \frac {i \sqrt {3}-1}{2 \left (2 x^{3}+c_1 \right )^{{1}/{3}} x} \\ \end{align*}

✓ Mathematica. Time used: 0.664 (sec). Leaf size: 79

ode=x*D[y[x],x]+y[x]==-2*x^6*y[x]^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{\sqrt [3]{x^3 \left (2 x^3+c_1\right )}} \\ y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{x^3 \left (2 x^3+c_1\right )}} \\ y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{x^3 \left (2 x^3+c_1\right )}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 2.593 (sec). Leaf size: 73

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**6*y(x)**4 + x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {\sqrt [3]{\frac {1}{x^{3} \left (C_{1} + 2 x^{3}\right )}} \left (-1 - \sqrt {3} i\right )}{2}, \ y{\left (x \right )} = \frac {\sqrt [3]{\frac {1}{x^{3} \left (C_{1} + 2 x^{3}\right )}} \left (-1 + \sqrt {3} i\right )}{2}, \ y{\left (x \right )} = \sqrt [3]{\frac {1}{x^{3} \left (C_{1} + 2 x^{3}\right )}}\right ] \]