60.2.176 problem 752
Internal
problem
ID
[10750]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
752
Date
solved
:
Sunday, March 30, 2025 at 06:33:21 PM
CAS
classification
:
unknown
\begin{align*} y^{\prime }&=\frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )} \end{align*}
✓ Maple. Time used: 0.058 (sec). Leaf size: 723
ode:=diff(y(x),x) = cos(y(x))/(x*sin(y(x))-1)*(cos(y(x))*x^3-x-1)/(1+x);
dsolve(ode,y(x), singsol=all);
\begin{align*} \text {Solution too large to show}\end{align*}
✓ Mathematica. Time used: 5.405 (sec). Leaf size: 867
ode=D[y[x],x] == (Cos[y[x]]*(-1 - x + x^3*Cos[y[x]]))/((1 + x)*(-1 + x*Sin[y[x]]));
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \tan ^{-1}\left (\frac {6 \left (2 x^4-3 x^3+6 x^2+\sqrt {4 x^6-12 x^5+33 x^4+12 (-3+2 c_1) x^3-36 c_1 x^2-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)+36 \log ^2(x+1)+72 c_1 x+36 \left (1+c_1{}^2\right )}-6 x \log (x+1)+6 c_1 x\right )}{4 x^6-12 x^5+33 x^4+12 (-3+2 c_1) x^3-36 (-1+c_1) x^2-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)+36 \log ^2(x+1)+72 c_1 x+36 \left (1+c_1{}^2\right )},x-\frac {\left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ) \left (2 x^4-3 x^3+6 x^2+\sqrt {4 x^6-12 x^5+33 x^4+12 (-3+2 c_1) x^3-36 c_1 x^2-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)+36 \log ^2(x+1)+72 c_1 x+36 \left (1+c_1{}^2\right )}-6 x \log (x+1)+6 c_1 x\right )}{4 x^6-12 x^5+33 x^4+12 (-3+2 c_1) x^3-36 (-1+c_1) x^2-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)+36 \log ^2(x+1)+72 c_1 x+36 \left (1+c_1{}^2\right )}\right ) \\
y(x)\to \tan ^{-1}\left (-\frac {6 \left (-2 x^4+3 x^3-6 x^2+\sqrt {4 x^6-12 x^5+33 x^4+12 (-3+2 c_1) x^3-36 c_1 x^2-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)+36 \log ^2(x+1)+72 c_1 x+36 \left (1+c_1{}^2\right )}+6 x \log (x+1)-6 c_1 x\right )}{4 x^6-12 x^5+33 x^4+12 (-3+2 c_1) x^3-36 (-1+c_1) x^2-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)+36 \log ^2(x+1)+72 c_1 x+36 \left (1+c_1{}^2\right )},x-\frac {\left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ) \left (2 x^4-3 x^3+6 x^2-\sqrt {4 x^6-12 x^5+33 x^4+12 (-3+2 c_1) x^3-36 c_1 x^2-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)+36 \log ^2(x+1)+72 c_1 x+36 \left (1+c_1{}^2\right )}-6 x \log (x+1)+6 c_1 x\right )}{4 x^6-12 x^5+33 x^4+12 (-3+2 c_1) x^3-36 (-1+c_1) x^2-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)+36 \log ^2(x+1)+72 c_1 x+36 \left (1+c_1{}^2\right )}\right ) \\
y(x)\to -\frac {\pi }{2} \\
y(x)\to \frac {\pi }{2} \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(Derivative(y(x), x) - (x**3*cos(y(x)) - x - 1)*cos(y(x))/((x + 1)*(x*sin(y(x)) - 1)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out