60.1.258 problem 263
Internal
problem
ID
[10272]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
263
Date
solved
:
Wednesday, March 05, 2025 at 08:51:26 AM
CAS
classification
:
[_rational, _Bernoulli]
\begin{align*} 2 x^{3}+y y^{\prime }+3 x^{2} y^{2}+7&=0 \end{align*}
✓ Maple. Time used: 0.056 (sec). Leaf size: 169
ode:=2*x^3+y(x)*diff(y(x),x)+3*x^2*y(x)^2+7 = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -\frac {2^{{5}/{6}} \sqrt {3}\, \sqrt {-80 \left (-x^{3}\right )^{{1}/{3}} \left (\frac {9 \left (-\frac {3 \,{\mathrm e}^{-2 x^{3}} c_{1}}{2}+x \right ) 2^{{1}/{3}} \Gamma \left (\frac {2}{3}\right ) \left (-x^{3}\right )^{{1}/{3}}}{40}+{\mathrm e}^{-2 x^{3}} x \left (\pi \sqrt {3}-\frac {3 \Gamma \left (\frac {1}{3}, -2 x^{3}\right ) \Gamma \left (\frac {2}{3}\right )}{2}\right )\right )}}{18 \sqrt {\Gamma \left (\frac {2}{3}\right )}\, \left (-x^{3}\right )^{{1}/{3}}} \\
y &= \frac {2^{{5}/{6}} \sqrt {3}\, \sqrt {-80 \left (-x^{3}\right )^{{1}/{3}} \left (\frac {9 \left (-\frac {3 \,{\mathrm e}^{-2 x^{3}} c_{1}}{2}+x \right ) 2^{{1}/{3}} \Gamma \left (\frac {2}{3}\right ) \left (-x^{3}\right )^{{1}/{3}}}{40}+{\mathrm e}^{-2 x^{3}} x \left (\pi \sqrt {3}-\frac {3 \Gamma \left (\frac {1}{3}, -2 x^{3}\right ) \Gamma \left (\frac {2}{3}\right )}{2}\right )\right )}}{18 \sqrt {\Gamma \left (\frac {2}{3}\right )}\, \left (-x^{3}\right )^{{1}/{3}}} \\
\end{align*}
✓ Mathematica. Time used: 4.857 (sec). Leaf size: 166
ode=2*x^3+y[x]*D[y[x],x]+3*x^2*y[x]^2+7==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\frac {\sqrt {\frac {e^{-2 x^3} \left (-7\ 2^{2/3} \left (-x^3\right )^{2/3} \Gamma \left (\frac {1}{3},-2 x^3\right )+2^{2/3} \left (-x^3\right )^{2/3} \Gamma \left (\frac {4}{3},-2 x^3\right )+3 c_1 x^2\right )}{x^2}}}{\sqrt {3}} \\
y(x)\to \frac {\sqrt {\frac {e^{-2 x^3} \left (-7\ 2^{2/3} \left (-x^3\right )^{2/3} \Gamma \left (\frac {1}{3},-2 x^3\right )+2^{2/3} \left (-x^3\right )^{2/3} \Gamma \left (\frac {4}{3},-2 x^3\right )+3 c_1 x^2\right )}{x^2}}}{\sqrt {3}} \\
\end{align*}
✓ Sympy. Time used: 2.321 (sec). Leaf size: 134
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(2*x**3 + 3*x**2*y(x)**2 + y(x)*Derivative(y(x), x) + 7,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {\sqrt {3} \sqrt {\left (C_{1} - 7 \cdot 2^{\frac {2}{3}} \gamma \left (\frac {1}{3}, 2 x^{3} e^{i \pi }\right ) + 2^{\frac {2}{3}} \gamma \left (\frac {4}{3}, 2 x^{3} e^{i \pi }\right )\right ) e^{- 2 x^{3} - \frac {i \pi }{3}}}}{3}, \ y{\left (x \right )} = \frac {\sqrt {3} \sqrt {\left (C_{1} - 7 \cdot 2^{\frac {2}{3}} \gamma \left (\frac {1}{3}, 2 x^{3} e^{i \pi }\right ) + 2^{\frac {2}{3}} \gamma \left (\frac {4}{3}, 2 x^{3} e^{i \pi }\right )\right ) e^{- 2 x^{3} - \frac {i \pi }{3}}}}{3}\right ]
\]