60.1.430 problem 441
Internal
problem
ID
[10444]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
441
Date
solved
:
Wednesday, March 05, 2025 at 10:49:33 AM
CAS
classification
:
[_separable]
\begin{align*} x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 y \left (y+2\right )&=0 \end{align*}
✓ Maple. Time used: 0.051 (sec). Leaf size: 83
ode:=x^2*diff(y(x),x)^2-4*x*(2+y(x))*diff(y(x),x)+4*y(x)*(2+y(x)) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -2 \\
y &= \frac {-2 \sqrt {2}\, \sqrt {c_{1} x^{2}}+x^{2}}{c_{1}} \\
y &= \frac {2 \sqrt {2}\, \sqrt {c_{1} x^{2}}+x^{2}}{c_{1}} \\
y &= \frac {\left (-2 c_{1} \sqrt {2}+x \right ) x}{c_{1}^{2}} \\
y &= \frac {x \left (2 c_{1} \sqrt {2}+x \right )}{c_{1}^{2}} \\
\end{align*}
✓ Mathematica. Time used: 0.188 (sec). Leaf size: 69
ode=4*y[x]*(2 + y[x]) - 4*x*(2 + y[x])*D[y[x],x] + x^2*D[y[x],x]^2==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to e^{-c_1} x \left (x-2 \sqrt {2} e^{\frac {c_1}{2}}\right ) \\
y(x)\to e^{c_1} x^2-2 \sqrt {2} e^{\frac {c_1}{2}} x \\
y(x)\to -2 \\
y(x)\to 0 \\
\end{align*}
✓ Sympy. Time used: 29.287 (sec). Leaf size: 160
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x**2*Derivative(y(x), x)**2 - 4*x*(y(x) + 2)*Derivative(y(x), x) + 4*(y(x) + 2)*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = x \left (- C_{1} x + 2 \sqrt {2} \sqrt {- C_{1}}\right ), \ y{\left (x \right )} = x \left (- C_{1} x - 2 \sqrt {2} \sqrt {- C_{1}}\right ), \ y{\left (x \right )} = x \left (- 2 \sqrt {2} \sqrt {C_{1}} + C_{1} x\right ), \ y{\left (x \right )} = x \left (2 \sqrt {2} \sqrt {C_{1}} + C_{1} x\right ), \ y{\left (x \right )} = x \left (- C_{1} x + 2 \sqrt {2} \sqrt {- C_{1}}\right ), \ y{\left (x \right )} = x \left (- C_{1} x - 2 \sqrt {2} \sqrt {- C_{1}}\right ), \ y{\left (x \right )} = x \left (- 2 \sqrt {2} \sqrt {C_{1}} + C_{1} x\right ), \ y{\left (x \right )} = x \left (2 \sqrt {2} \sqrt {C_{1}} + C_{1} x\right )\right ]
\]