60.1.42 problem 42
Internal
problem
ID
[10056]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
42
Date
solved
:
Sunday, March 30, 2025 at 02:58:17 PM
CAS
classification
:
[_Abel]
\begin{align*} y^{\prime }-x \left (x +2\right ) y^{3}-\left (x +3\right ) y^{2}&=0 \end{align*}
✓ Maple. Time used: 0.001 (sec). Leaf size: 53
ode:=diff(y(x),x)-x*(x+2)*y(x)^3-(x+3)*y(x)^2 = 0;
dsolve(ode,y(x), singsol=all);
\[
\frac {\frac {\sqrt {2+\left (x^{2}+2 x \right ) y}}{2}+\left (\operatorname {arctanh}\left (\frac {\sqrt {y}\, x}{\sqrt {2+\left (x^{2}+2 x \right ) y}}\right )+c_1 \right ) \sqrt {y}}{\sqrt {y}} = 0
\]
✓ Mathematica. Time used: 0.71 (sec). Leaf size: 485
ode=D[y[x],x] - x*(x+2)*y[x]^3 - (x+3)*y[x]^2==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [c_1=-\frac {\frac {i \sqrt {\frac {2}{\pi }} \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}} \left (\frac {\sinh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}-\cosh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}-\frac {i \sqrt {\frac {2}{\pi }} \left (\frac {x+1}{2}+\frac {1}{2}\right ) \sinh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}}{\frac {i \sqrt {\frac {2}{\pi }} \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}} \left (i \sinh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )-\frac {i \cosh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}-\frac {\sqrt {\frac {2}{\pi }} \left (\frac {x+1}{2}+\frac {1}{2}\right ) \cosh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}},y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x*(x + 2)*y(x)**3 - (x + 3)*y(x)**2 + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out