22.1.47 problem 48

Internal problem ID [4353]
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 : 48
Date solved : Tuesday, September 30, 2025 at 07:23:03 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.142 (sec). Leaf size: 2230

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 30.991 (sec). Leaf size: 318

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

\begin{align*} y(x)&\to \frac {c_1 x}{\sqrt [3]{-54 x^4+6 \sqrt {3} \sqrt {-x^8 \left (-27+2 c_1{}^3 x\right )}}}+\frac {\sqrt [3]{-9 x^4+\sqrt {3} \sqrt {-x^8 \left (-27+2 c_1{}^3 x\right )}}}{6^{2/3} x^2}\\ y(x)&\to \frac {i \left (\sqrt {3}+i\right ) \sqrt [3]{-9 x^4+\sqrt {3} \sqrt {-x^8 \left (-27+2 c_1{}^3 x\right )}}}{2\ 6^{2/3} x^2}-\frac {i \left (\sqrt {3}-i\right ) c_1 x}{2 \sqrt [3]{-54 x^4+6 \sqrt {3} \sqrt {-x^8 \left (-27+2 c_1{}^3 x\right )}}}\\ y(x)&\to \frac {i \left (\sqrt {3}+i\right ) c_1 x}{2 \sqrt [3]{-54 x^4+6 \sqrt {3} \sqrt {-x^8 \left (-27+2 c_1{}^3 x\right )}}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-9 x^4+\sqrt {3} \sqrt {-x^8 \left (-27+2 c_1{}^3 x\right )}}}{2\ 6^{2/3} x^2} \end{align*}

✗ Sympy

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

Timed Out