83.28.6 problem 6

Internal problem ID [19371]
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 : Tuesday, January 28, 2025 at 01:35:41 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

dsolve(diff(y(x),x$3)*csc(x)^2=1,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{3}}{12}-\frac {x}{8}+\frac {c_{1} x^{2}}{2}+c_{2} x +c_3 +\frac {\sin \left (2 x \right )}{16} \]

✓ Solution by Mathematica

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

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

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