28.1.74 problem 77

Internal problem ID [4380]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 77
Date solved : Tuesday, March 04, 2025 at 06:33:41 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 63

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

\begin{align*} y \left (x \right ) &= \left (x^{3} \left (c_{1} x +8\right )\right )^{{1}/{4}} \\ y \left (x \right ) &= -\left (x^{3} \left (c_{1} x +8\right )\right )^{{1}/{4}} \\ y \left (x \right ) &= -i \left (x^{3} \left (c_{1} x +8\right )\right )^{{1}/{4}} \\ y \left (x \right ) &= i \left (x^{3} \left (c_{1} x +8\right )\right )^{{1}/{4}} \\ \end{align*}

✓ Mathematica. Time used: 0.306 (sec). Leaf size: 88

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

\begin{align*} y(x)\to -x^{3/4} \sqrt [4]{8+c_1 x} \\ y(x)\to -i x^{3/4} \sqrt [4]{8+c_1 x} \\ y(x)\to i x^{3/4} \sqrt [4]{8+c_1 x} \\ y(x)\to x^{3/4} \sqrt [4]{8+c_1 x} \\ \end{align*}

✓ Sympy. Time used: 1.707 (sec). Leaf size: 61

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

\[ \left [ y{\left (x \right )} = - i \sqrt [4]{x^{3} \left (C_{1} x + 8\right )}, \ y{\left (x \right )} = i \sqrt [4]{x^{3} \left (C_{1} x + 8\right )}, \ y{\left (x \right )} = - \sqrt [4]{x^{3} \left (C_{1} x + 8\right )}, \ y{\left (x \right )} = \sqrt [4]{x^{3} \left (C_{1} x + 8\right )}\right ] \]