60.1.449 problem 462
Internal
problem
ID
[10463]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
462
Date
solved
:
Sunday, March 30, 2025 at 04:50:40 PM
CAS
classification
:
[_quadrature]
\begin{align*} y {y^{\prime }}^{2}-1&=0 \end{align*}
✓ Maple. Time used: 0.029 (sec). Leaf size: 27
ode:=y(x)*diff(y(x),x)^2-1 = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
x -\frac {2 y^{{3}/{2}}}{3}-c_1 &= 0 \\
x +\frac {2 y^{{3}/{2}}}{3}-c_1 &= 0 \\
\end{align*}
✓ Mathematica. Time used: 0.032 (sec). Leaf size: 43
ode=-1 + y[x]*D[y[x],x]^2==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \left (\frac {3}{2}\right )^{2/3} (-x+c_1){}^{2/3} \\
y(x)\to \left (\frac {3}{2}\right )^{2/3} (x+c_1){}^{2/3} \\
\end{align*}
✓ Sympy. Time used: 16.107 (sec). Leaf size: 160
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(y(x)*Derivative(y(x), x)**2 - 1,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} \left (C_{1} + x\right )^{\frac {2}{3}}}{2}, \ y{\left (x \right )} = \frac {\sqrt [3]{2} \left (- 3^{\frac {2}{3}} + 3 \sqrt [6]{3} i\right ) \left (C_{1} + x\right )^{\frac {2}{3}}}{4}, \ y{\left (x \right )} = \frac {\sqrt [3]{2} \left (- 3^{\frac {2}{3}} - 3 \sqrt [6]{3} i\right ) \left (C_{1} + x\right )^{\frac {2}{3}}}{4}, \ y{\left (x \right )} = \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} \left (C_{1} + x\right )^{\frac {2}{3}}}{2}, \ y{\left (x \right )} = \frac {\sqrt [3]{2} \left (- 3^{\frac {2}{3}} + 3 \sqrt [6]{3} i\right ) \left (C_{1} + x\right )^{\frac {2}{3}}}{4}, \ y{\left (x \right )} = \frac {\sqrt [3]{2} \left (- 3^{\frac {2}{3}} - 3 \sqrt [6]{3} i\right ) \left (C_{1} + x\right )^{\frac {2}{3}}}{4}\right ]
\]