73.3.10 problem 4.3 (j)
Internal
problem
ID
[14973]
Book
:
Ordinary
Differential
Equations.
An
introduction
to
the
fundamentals.
Kenneth
B.
Howell.
second
edition.
CRC
Press.
FL,
USA.
2020
Section
:
Chapter
4.
SEPARABLE
FIRST
ORDER
EQUATIONS.
Additional
exercises.
page
90
Problem
number
:
4.3
(j)
Date
solved
:
Monday, March 31, 2025 at 01:09:28 PM
CAS
classification
:
[_separable]
\begin{align*} y y^{\prime }&={\mathrm e}^{x -3 y^{2}} \end{align*}
✓ Maple. Time used: 0.006 (sec). Leaf size: 41
ode:=y(x)*diff(y(x),x) = exp(x-3*y(x)^2);
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -\frac {\sqrt {3}\, \sqrt {\ln \left (2\right )+\ln \left (3\right )+\ln \left ({\mathrm e}^{x}+c_1 \right )}}{3} \\
y &= \frac {\sqrt {3}\, \sqrt {\ln \left (2\right )+\ln \left (3\right )+\ln \left ({\mathrm e}^{x}+c_1 \right )}}{3} \\
\end{align*}
✓ Mathematica. Time used: 3.56 (sec). Leaf size: 48
ode=y[x]*D[y[x],x]==Exp[x-3*y[x]^2];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\frac {\sqrt {\log \left (6 \left (e^x+c_1\right )\right )}}{\sqrt {3}} \\
y(x)\to \frac {\sqrt {\log \left (6 \left (e^x+c_1\right )\right )}}{\sqrt {3}} \\
\end{align*}
✓ Sympy. Time used: 24.919 (sec). Leaf size: 185
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(y(x)*Derivative(y(x), x) - exp(x - 3*y(x)**2),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {\sqrt {3} \sqrt {\log {\left (C_{1} + 6 e^{x} \right )}}}{3}, \ y{\left (x \right )} = \frac {\sqrt {3} \sqrt {\log {\left (C_{1} + 6 e^{x} \right )}}}{3}, \ y{\left (x \right )} = - \sqrt {\log {\left (\frac {\left (- \sqrt [3]{6} - \sqrt [3]{2} \cdot 3^{\frac {5}{6}} i\right ) \sqrt [3]{C_{1} + e^{x}}}{2} \right )}}, \ y{\left (x \right )} = \sqrt {\log {\left (\frac {\left (- \sqrt [3]{6} - \sqrt [3]{2} \cdot 3^{\frac {5}{6}} i\right ) \sqrt [3]{C_{1} + e^{x}}}{2} \right )}}, \ y{\left (x \right )} = - \sqrt {\log {\left (\frac {\left (- \sqrt [3]{6} + \sqrt [3]{2} \cdot 3^{\frac {5}{6}} i\right ) \sqrt [3]{C_{1} + e^{x}}}{2} \right )}}, \ y{\left (x \right )} = \sqrt {\log {\left (\frac {\left (- \sqrt [3]{6} + \sqrt [3]{2} \cdot 3^{\frac {5}{6}} i\right ) \sqrt [3]{C_{1} + e^{x}}}{2} \right )}}\right ]
\]