60.1.300 problem 306
Internal
problem
ID
[10314]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
306
Date
solved
:
Sunday, March 30, 2025 at 03:58:57 PM
CAS
classification
:
[[_homogeneous, `class A`], _rational, _dAlembert]
\begin{align*} \left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y&=0 \end{align*}
✓ Maple. Time used: 0.268 (sec). Leaf size: 195
ode:=(y(x)^3-x^3)*diff(y(x),x)-x^2*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {\left (c_1 \,x^{3}-\sqrt {c_1^{2} x^{6}+1}\right )^{{1}/{3}}}{c_1^{{1}/{3}}} \\
y &= \frac {\left (c_1 \,x^{3}+\sqrt {c_1^{2} x^{6}+1}\right )^{{1}/{3}}}{c_1^{{1}/{3}}} \\
y &= -\frac {\left (c_1 \,x^{3}-\sqrt {c_1^{2} x^{6}+1}\right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2 c_1^{{1}/{3}}} \\
y &= \frac {\left (c_1 \,x^{3}-\sqrt {c_1^{2} x^{6}+1}\right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{2 c_1^{{1}/{3}}} \\
y &= -\frac {\left (c_1 \,x^{3}+\sqrt {c_1^{2} x^{6}+1}\right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2 c_1^{{1}/{3}}} \\
y &= \frac {\left (c_1 \,x^{3}+\sqrt {c_1^{2} x^{6}+1}\right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{2 c_1^{{1}/{3}}} \\
\end{align*}
✓ Mathematica. Time used: 0.113 (sec). Leaf size: 48
ode=-(x^2*y[x]) + (-x^3 + y[x]^3)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {(K[1]-1) \left (K[1]^2+K[1]+1\right )}{K[1] \left (K[1]^3-2\right )}dK[1]=-\log (x)+c_1,y(x)\right ]
\]
✓ Sympy. Time used: 11.565 (sec). Leaf size: 146
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x**2*y(x) + (-x**3 + y(x)**3)*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{x^{3} - \sqrt {C_{1} + x^{6}}}}{2}, \ y{\left (x \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{x^{3} + \sqrt {C_{1} + x^{6}}}}{2}, \ y{\left (x \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{x^{3} - \sqrt {C_{1} + x^{6}}}}{2}, \ y{\left (x \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{x^{3} + \sqrt {C_{1} + x^{6}}}}{2}, \ y{\left (x \right )} = \sqrt [3]{x^{3} - \sqrt {C_{1} + x^{6}}}, \ y{\left (x \right )} = \sqrt [3]{x^{3} + \sqrt {C_{1} + x^{6}}}\right ]
\]