88.9.14 problem 14
Internal
problem
ID
[24034]
Book
:
Elementary
Differential
Equations.
By
Lee
Roy
Wilcox
and
Herbert
J.
Curtis.
1961
first
edition.
International
texbook
company.
Scranton,
Penn.
USA.
CAT
number
61-15976
Section
:
Chapter
2.
Differential
equations
of
first
order.
Exercise
at
page
48
Problem
number
:
14
Date
solved
:
Thursday, October 02, 2025 at 09:54:57 PM
CAS
classification
:
[_quadrature]
\begin{align*} y^{5} y^{\prime }+5 y^{6}&=1 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 129
ode:=y(x)^5*diff(y(x),x)+5*y(x)^6 = 1;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -\frac {\left (15625 \,{\mathrm e}^{-30 x} c_1 +3125\right )^{{1}/{6}}}{5} \\
y &= \frac {\left (15625 \,{\mathrm e}^{-30 x} c_1 +3125\right )^{{1}/{6}}}{5} \\
y &= \frac {\left (-\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) \left (15625 \,{\mathrm e}^{-30 x} c_1 +3125\right )^{{1}/{6}}}{5} \\
y &= \frac {\left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) \left (15625 \,{\mathrm e}^{-30 x} c_1 +3125\right )^{{1}/{6}}}{5} \\
y &= \frac {\left (\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) \left (15625 \,{\mathrm e}^{-30 x} c_1 +3125\right )^{{1}/{6}}}{5} \\
y &= \frac {\left (\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) \left (15625 \,{\mathrm e}^{-30 x} c_1 +3125\right )^{{1}/{6}}}{5} \\
\end{align*}
✓ Mathematica. Time used: 0.658 (sec). Leaf size: 262
ode=y[x]^5*D[y[x],{x,1}]+5*y[x]^6==1;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to -\frac {\sqrt [6]{1+e^{30 (-x+c_1)}}}{\sqrt [6]{5}}\\ y(x)&\to \frac {\sqrt [6]{1+e^{30 (-x+c_1)}}}{\sqrt [6]{5}}\\ y(x)&\to -\frac {\sqrt [3]{-1} \sqrt [6]{1+e^{30 (-x+c_1)}}}{\sqrt [6]{5}}\\ y(x)&\to \frac {\sqrt [3]{-1} \sqrt [6]{1+e^{30 (-x+c_1)}}}{\sqrt [6]{5}}\\ y(x)&\to -\frac {(-1)^{2/3} \sqrt [6]{1+e^{30 (-x+c_1)}}}{\sqrt [6]{5}}\\ y(x)&\to \frac {(-1)^{2/3} \sqrt [6]{1+e^{30 (-x+c_1)}}}{\sqrt [6]{5}}\\ y(x)&\to -\frac {1}{\sqrt [6]{5}}\\ y(x)&\to \frac {1}{\sqrt [6]{5}}\\ y(x)&\to -\frac {\sqrt [3]{-1}}{\sqrt [6]{5}}\\ y(x)&\to \frac {\sqrt [3]{-1}}{\sqrt [6]{5}}\\ y(x)&\to -\frac {(-1)^{2/3}}{\sqrt [6]{5}}\\ y(x)&\to \frac {(-1)^{2/3}}{\sqrt [6]{5}} \end{align*}
✓ Sympy. Time used: 5.119 (sec). Leaf size: 160
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(5*y(x)**6 + y(x)**5*Derivative(y(x), x) - 1,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {5^{\frac {5}{6}} \sqrt [6]{C_{1} e^{- 30 x} + 1}}{5}, \ y{\left (x \right )} = \frac {5^{\frac {5}{6}} \sqrt [6]{C_{1} e^{- 30 x} + 1}}{5}, \ y{\left (x \right )} = \frac {5^{\frac {5}{6}} \left (-1 - \sqrt {3} i\right ) \sqrt [6]{C_{1} e^{- 30 x} + 1}}{10}, \ y{\left (x \right )} = \frac {5^{\frac {5}{6}} \left (-1 + \sqrt {3} i\right ) \sqrt [6]{C_{1} e^{- 30 x} + 1}}{10}, \ y{\left (x \right )} = \frac {5^{\frac {5}{6}} \left (1 - \sqrt {3} i\right ) \sqrt [6]{C_{1} e^{- 30 x} + 1}}{10}, \ y{\left (x \right )} = \frac {5^{\frac {5}{6}} \left (1 + \sqrt {3} i\right ) \sqrt [6]{C_{1} e^{- 30 x} + 1}}{10}\right ]
\]