29.29.12 problem 834
Internal
problem
ID
[5417]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
29
Problem
number
:
834
Date
solved
:
Tuesday, March 04, 2025 at 09:36:18 PM
CAS
classification
:
[_quadrature]
\begin{align*} 2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right )&=0 \end{align*}
✓ Maple. Time used: 1.327 (sec). Leaf size: 61
ode:=2*diff(y(x),x)^2+2*(6*y(x)-1)*diff(y(x),x)+3*y(x)*(6*y(x)-1) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y \left (x \right ) &= {\frac {1}{6}} \\
y \left (x \right ) &= -\frac {\left (\sqrt {6}\, {\mathrm e}^{\frac {3 x}{2}+\frac {3 c_{1}}{2}}+3 \,{\mathrm e}^{3 c_{1}}\right ) {\mathrm e}^{-3 x}}{3} \\
y \left (x \right ) &= \frac {\left (\sqrt {6}\, {\mathrm e}^{\frac {3 x}{2}+\frac {3 c_{1}}{2}}-3 \,{\mathrm e}^{3 c_{1}}\right ) {\mathrm e}^{-3 x}}{3} \\
\end{align*}
✓ Mathematica. Time used: 0.263 (sec). Leaf size: 81
ode=2 (D[y[x],x])^2+2(6 y[x]-1)D[y[x],x]+3 y[x](6 y[x]-1)==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\frac {1}{6} e^{-3 x+3 c_1} \left (2 e^{3 x/2}+e^{3 c_1}\right ) \\
y(x)\to \frac {1}{6} e^{-3 (x+2 c_1)} \left (-1+2 e^{\frac {3 x}{2}+3 c_1}\right ) \\
y(x)\to 0 \\
y(x)\to \frac {1}{6} \\
\end{align*}
✓ Sympy. Time used: 61.585 (sec). Leaf size: 269
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((12*y(x) - 2)*Derivative(y(x), x) + (18*y(x) - 3)*y(x) + 2*Derivative(y(x), x)**2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {- e^{C_{1} + 9 x}} e^{- 6 x}}{3} + \frac {e^{C_{1} - 3 x}}{3}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {- e^{C_{1} + 9 x}} e^{- 6 x}}{3} + \frac {e^{C_{1} - 3 x}}{3}, \ y{\left (x \right )} = - \frac {e^{C_{1} - 3 x}}{3} - \frac {\sqrt {2} e^{- 6 x} \sqrt {e^{C_{1} + 9 x}}}{3}, \ y{\left (x \right )} = - \frac {e^{C_{1} - 3 x}}{3} + \frac {\sqrt {2} e^{- 6 x} \sqrt {e^{C_{1} + 9 x}}}{3}, \ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {- e^{C_{1} + 9 x}} e^{- 6 x}}{3} + \frac {e^{C_{1} - 3 x}}{3}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {- e^{C_{1} + 9 x}} e^{- 6 x}}{3} + \frac {e^{C_{1} - 3 x}}{3}, \ y{\left (x \right )} = - \frac {e^{C_{1} - 3 x}}{3} - \frac {\sqrt {2} e^{- 6 x} \sqrt {e^{C_{1} + 9 x}}}{3}, \ y{\left (x \right )} = - \frac {e^{C_{1} - 3 x}}{3} + \frac {\sqrt {2} e^{- 6 x} \sqrt {e^{C_{1} + 9 x}}}{3}\right ]
\]