83.28.6 problem 6

Internal problem ID [19300]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (B) at page 106
Problem number : 6
Date solved : Monday, March 31, 2025 at 07:06:03 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime } \csc \left (x \right )^{2}&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

ode:=diff(diff(diff(y(x),x),x),x)*csc(x)^2 = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{12}-\frac {x}{8}+\frac {c_1 \,x^{2}}{2}+c_2 x +c_3 +\frac {\sin \left (2 x \right )}{16} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 37

ode=D[y[x],{x,3}]*Csc[x]^2==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^3}{12}+c_3 x^2+\left (\frac {1}{8}+c_2\right ) x+\frac {1}{8} \sin (x) \cos (x)+c_1 \]

✓ Sympy. Time used: 0.665 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-1 + Derivative(y(x), (x, 3))/sin(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + \frac {x^{3}}{12} + \frac {x}{8} + \frac {\sin {\left (2 x \right )}}{16} \]