57.1.55 problem 55
Internal
problem
ID
[9039]
Book
:
First
order
enumerated
odes
Section
:
section
1
Problem
number
:
55
Date
solved
:
Sunday, March 30, 2025 at 01:59:58 PM
CAS
classification
:
[[_homogeneous, `class G`]]
\begin{align*} {y^{\prime }}^{2}&=\frac {1}{y x} \end{align*}
✓ Maple. Time used: 0.040 (sec). Leaf size: 51
ode:=diff(y(x),x)^2 = 1/x/y(x);
dsolve(ode,y(x), singsol=all);
\begin{align*}
\frac {y \sqrt {y x}-c_1 \sqrt {x}-3 x}{\sqrt {x}} &= 0 \\
\frac {y \sqrt {y x}-c_1 \sqrt {x}+3 x}{\sqrt {x}} &= 0 \\
\end{align*}
✓ Mathematica. Time used: 3.346 (sec). Leaf size: 53
ode=(D[y[x],x])^2==1/(y[x]*x);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (-2 \sqrt {x}+c_1\right ){}^{2/3} \\
y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (2 \sqrt {x}+c_1\right ){}^{2/3} \\
\end{align*}
✓ Sympy. Time used: 52.023 (sec). Leaf size: 374
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(Derivative(y(x), x)**2 - 1/(x*y(x)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{\frac {9 C_{1}^{2}}{4} - 9 C_{1} \sqrt {x} + 9 x}}{2}, \ y{\left (x \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{\frac {9 C_{1}^{2}}{4} - 9 C_{1} \sqrt {x} + 9 x}}{2}, \ y{\left (x \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{\frac {9 C_{1}^{2}}{4} + 9 C_{1} \sqrt {x} + 9 x}}{2}, \ y{\left (x \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{\frac {9 C_{1}^{2}}{4} + 9 C_{1} \sqrt {x} + 9 x}}{2}, \ y{\left (x \right )} = \sqrt [3]{\frac {9 C_{1}^{2}}{4} - 9 C_{1} \sqrt {x} + 9 x}, \ y{\left (x \right )} = \sqrt [3]{\frac {9 C_{1}^{2}}{4} + 9 C_{1} \sqrt {x} + 9 x}, \ y{\left (x \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{\frac {9 C_{1}^{2}}{4} - 9 C_{1} \sqrt {x} + 9 x}}{2}, \ y{\left (x \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{\frac {9 C_{1}^{2}}{4} - 9 C_{1} \sqrt {x} + 9 x}}{2}, \ y{\left (x \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{\frac {9 C_{1}^{2}}{4} + 9 C_{1} \sqrt {x} + 9 x}}{2}, \ y{\left (x \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{\frac {9 C_{1}^{2}}{4} + 9 C_{1} \sqrt {x} + 9 x}}{2}, \ y{\left (x \right )} = \sqrt [3]{\frac {9 C_{1}^{2}}{4} - 9 C_{1} \sqrt {x} + 9 x}, \ y{\left (x \right )} = \sqrt [3]{\frac {9 C_{1}^{2}}{4} + 9 C_{1} \sqrt {x} + 9 x}\right ]
\]