29.32.9 problem 943
Internal
problem
ID
[5521]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
32
Problem
number
:
943
Date
solved
:
Sunday, March 30, 2025 at 08:29:23 AM
CAS
classification
:
[[_1st_order, _with_linear_symmetries]]
\begin{align*} y {y^{\prime }}^{2}&={\mathrm e}^{2 x} \end{align*}
✓ Maple. Time used: 0.045 (sec). Leaf size: 67
ode:=y(x)*diff(y(x),x)^2 = exp(2*x);
dsolve(ode,y(x), singsol=all);
\begin{align*}
\frac {2 y^{2}+3 c_1 \sqrt {y}-3 \sqrt {y \,{\mathrm e}^{2 x}}}{3 \sqrt {y}} &= 0 \\
\frac {2 y^{2}+3 c_1 \sqrt {y}+3 \sqrt {y \,{\mathrm e}^{2 x}}}{3 \sqrt {y}} &= 0 \\
\end{align*}
✓ Mathematica. Time used: 2.139 (sec). Leaf size: 47
ode=y[x] (D[y[x],x])^2==Exp[2 x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (-e^x+c_1\right ){}^{2/3} \\
y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (e^x+c_1\right ){}^{2/3} \\
\end{align*}
✓ Sympy. Time used: 24.131 (sec). Leaf size: 170
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(y(x)*Derivative(y(x), x)**2 - exp(2*x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} \left (C_{1} - e^{x}\right )^{\frac {2}{3}}}{2}, \ y{\left (x \right )} = \frac {\sqrt [3]{2} \left (- 3^{\frac {2}{3}} + 3 \sqrt [6]{3} i\right ) \left (C_{1} - e^{x}\right )^{\frac {2}{3}}}{4}, \ y{\left (x \right )} = \frac {\sqrt [3]{2} \left (- 3^{\frac {2}{3}} - 3 \sqrt [6]{3} i\right ) \left (C_{1} - e^{x}\right )^{\frac {2}{3}}}{4}, \ y{\left (x \right )} = \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} \left (C_{1} + e^{x}\right )^{\frac {2}{3}}}{2}, \ y{\left (x \right )} = \frac {\sqrt [3]{2} \left (- 3^{\frac {2}{3}} + 3 \sqrt [6]{3} i\right ) \left (C_{1} + e^{x}\right )^{\frac {2}{3}}}{4}, \ y{\left (x \right )} = \frac {\sqrt [3]{2} \left (- 3^{\frac {2}{3}} - 3 \sqrt [6]{3} i\right ) \left (C_{1} + e^{x}\right )^{\frac {2}{3}}}{4}\right ]
\]