38.6.15 problem 15

Internal problem ID [8445]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 05:36:59 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y-4 \left (x +y^{6}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 993

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

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

✓ Mathematica. Time used: 56.001 (sec). Leaf size: 827

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

\begin{align*} y(x)&\to -\frac {\sqrt {\frac {c_1{}^2}{\sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}}+\sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}-c_1}}{\sqrt {6}}\\ y(x)&\to \frac {\sqrt {\frac {c_1{}^2}{\sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}}+\sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}-c_1}}{\sqrt {6}}\\ y(x)&\to -\frac {\sqrt {-\frac {i \left (\sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}+c_1\right ) \left (\left (\sqrt {3}-i\right ) \sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}-\left (\sqrt {3}+i\right ) c_1\right )}{\sqrt [3]{54 x+6 \sqrt {3} \sqrt {x \left (27 x-c_1{}^3\right )}-c_1{}^3}}}}{2 \sqrt {3}}\\ y(x)&\to \frac {\sqrt {-\frac {i \left (\sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}+c_1\right ) \left (\left (\sqrt {3}-i\right ) \sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}-\left (\sqrt {3}+i\right ) c_1\right )}{\sqrt [3]{54 x+6 \sqrt {3} \sqrt {x \left (27 x-c_1{}^3\right )}-c_1{}^3}}}}{2 \sqrt {3}}\\ y(x)&\to -\frac {\sqrt {\frac {i \left (\sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}+c_1\right ) \left (\left (\sqrt {3}+i\right ) \sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}-\left (\sqrt {3}-i\right ) c_1\right )}{\sqrt [3]{54 x+6 \sqrt {3} \sqrt {x \left (27 x-c_1{}^3\right )}-c_1{}^3}}}}{2 \sqrt {3}}\\ y(x)&\to \frac {\sqrt {\frac {i \left (\sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}+c_1\right ) \left (\left (\sqrt {3}+i\right ) \sqrt [3]{54 x+6 \sqrt {3} \sqrt {-x \left (-27 x+c_1{}^3\right )}-c_1{}^3}-\left (\sqrt {3}-i\right ) c_1\right )}{\sqrt [3]{54 x+6 \sqrt {3} \sqrt {x \left (27 x-c_1{}^3\right )}-c_1{}^3}}}}{2 \sqrt {3}}\\ y(x)&\to 0 \end{align*}

✗ Sympy

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

Timed Out