73.7.15 problem 15
Internal
problem
ID
[15094]
Book
:
Ordinary
Differential
Equations.
An
introduction
to
the
fundamentals.
Kenneth
B.
Howell.
second
edition.
CRC
Press.
FL,
USA.
2020
Section
:
Chapter
8.
Review
exercises
for
part
of
part
II.
page
143
Problem
number
:
15
Date
solved
:
Thursday, March 13, 2025 at 05:37:44 AM
CAS
classification
:
[_quadrature]
\begin{align*} \left (y^{2}-4\right ) y^{\prime }&=y \end{align*}
✓ Maple. Time used: 0.036 (sec). Leaf size: 39
ode:=(y(x)^2-4)*diff(y(x),x) = y(x);
dsolve(ode,y(x), singsol=all);
\[
y = \frac {2 \,{\mathrm e}^{-\frac {x}{4}-\frac {c_{1}}{4}}}{\sqrt {-\frac {{\mathrm e}^{-\frac {x}{2}-\frac {c_{1}}{2}}}{\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {x}{2}-\frac {c_{1}}{2}}}{4}\right )}}}
\]
✓ Mathematica. Time used: 28.001 (sec). Leaf size: 246
ode=(y[x]^2-4)*D[y[x],x]==y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -2 i \sqrt {W\left (-\frac {1}{4} \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\
y(x)\to 2 i \sqrt {W\left (-\frac {1}{4} \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\
y(x)\to -2 i \sqrt {W\left (-\frac {1}{4} i \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\
y(x)\to 2 i \sqrt {W\left (-\frac {1}{4} i \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\
y(x)\to -2 i \sqrt {W\left (\frac {1}{4} i \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\
y(x)\to 2 i \sqrt {W\left (\frac {1}{4} i \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\
y(x)\to -2 i \sqrt {W\left (\frac {1}{4} \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\
y(x)\to 2 i \sqrt {W\left (\frac {1}{4} \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\
y(x)\to 0 \\
\end{align*}
✓ Sympy. Time used: 1.506 (sec). Leaf size: 56
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((y(x)**2 - 4)*Derivative(y(x), x) - y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = e^{- \frac {C_{1}}{4} - \frac {x}{4} - \frac {W\left (- \frac {e^{- \frac {C_{1}}{2} - \frac {x}{2}}}{4}\right )}{2}}, \ y{\left (x \right )} = e^{- \frac {C_{1}}{4} - \frac {x}{4} - \frac {W\left (\frac {e^{- \frac {C_{1}}{2} - \frac {x}{2}}}{4}\right )}{2}}\right ]
\]