78.8.26 problem 26

Internal problem ID [18153]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 26
Date solved : Monday, March 31, 2025 at 05:15:13 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 56

ode:=x^2*y(x)^4+x^6-x^3*y(x)^3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \left (4 \ln \left (x \right )+c_1 \right )^{{1}/{4}} x \\ y &= -\left (4 \ln \left (x \right )+c_1 \right )^{{1}/{4}} x \\ y &= -i \left (4 \ln \left (x \right )+c_1 \right )^{{1}/{4}} x \\ y &= i \left (4 \ln \left (x \right )+c_1 \right )^{{1}/{4}} x \\ \end{align*}

✓ Mathematica. Time used: 0.179 (sec). Leaf size: 76

ode=(x^2*y[x]^4+x^6)-(x^3*y[x]^3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -x \sqrt [4]{4 \log (x)+c_1} \\ y(x)\to -i x \sqrt [4]{4 \log (x)+c_1} \\ y(x)\to i x \sqrt [4]{4 \log (x)+c_1} \\ y(x)\to x \sqrt [4]{4 \log (x)+c_1} \\ \end{align*}

✓ Sympy. Time used: 2.488 (sec). Leaf size: 68

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**6 - x**3*y(x)**3*Derivative(y(x), x) + x**2*y(x)**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - i \sqrt [4]{x^{4} \left (C_{1} + 4 \log {\left (x \right )}\right )}, \ y{\left (x \right )} = i \sqrt [4]{x^{4} \left (C_{1} + 4 \log {\left (x \right )}\right )}, \ y{\left (x \right )} = - \sqrt [4]{x^{4} \left (C_{1} + 4 \log {\left (x \right )}\right )}, \ y{\left (x \right )} = \sqrt [4]{x^{4} \left (C_{1} + 4 \log {\left (x \right )}\right )}\right ] \]