60.1.387 problem 398
Internal
problem
ID
[10401]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
398
Date
solved
:
Sunday, March 30, 2025 at 04:36:57 PM
CAS
classification
:
[[_1st_order, _with_linear_symmetries]]
\begin{align*} {y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \end{align*}
✓ Maple. Time used: 0.106 (sec). Leaf size: 201
ode:=diff(y(x),x)^2-3*x*y(x)^(2/3)*diff(y(x),x)+9*y(x)^(5/3) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {x^{6}}{64} \\
y &= 0 \\
\frac {-x \left (c_1 -y^{{1}/{3}}\right ) \sqrt {y^{{4}/{3}} \left (x^{2}-4 y^{{1}/{3}}\right )}-y^{{2}/{3}} c_1 \,x^{2}+4 y^{{4}/{3}}+\left (-x^{2}+4 c_1 \right ) y}{y^{{2}/{3}} x^{2}+x \sqrt {y^{{4}/{3}} \left (x^{2}-4 y^{{1}/{3}}\right )}-4 y} &= 0 \\
\frac {x \left (c_1 -y^{{1}/{3}}\right ) \sqrt {y^{{4}/{3}} \left (x^{2}-4 y^{{1}/{3}}\right )}-y^{{2}/{3}} c_1 \,x^{2}+4 y^{{4}/{3}}+\left (-x^{2}+4 c_1 \right ) y}{y^{{2}/{3}} x^{2}-x \sqrt {y^{{4}/{3}} \left (x^{2}-4 y^{{1}/{3}}\right )}-4 y} &= 0 \\
\end{align*}
✓ Mathematica. Time used: 9.334 (sec). Leaf size: 418
ode=9*y[x]^(5/3) - 3*x*y[x]^(2/3)*D[y[x],x] + D[y[x],x]^2==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
\text {Solve}\left [\frac {\sqrt {x^2-4 \sqrt [3]{y(x)}} \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}}{8 y(x)-2 x^2 y(x)^{2/3}}+\frac {\sqrt {\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}} \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}-x\right )}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}+\log \left (4 y(x)^{4/3}-x^2 y(x)\right )-\log \left (x^2 \left (-y(x)^{2/3}\right )+\sqrt {x^2-4 \sqrt [3]{y(x)}} \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}+4 y(x)\right )&=c_1,y(x)\right ] \\
\text {Solve}\left [\frac {1}{6} \left (\frac {3 \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}+6 \log \left (4 y(x)^{4/3}-x^2 y(x)\right )-6 \log \left (x^2 y(x)^{2/3}+\sqrt {x^2-4 \sqrt [3]{y(x)}} \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}-4 y(x)\right )\right )-\frac {\sqrt {\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}} \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}-x\right )}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}&=c_1,y(x)\right ] \\
y(x)\to 0 \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-3*x*y(x)**(2/3)*Derivative(y(x), x) + 9*y(x)**(5/3) + Derivative(y(x), x)**2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out