83.35.5 problem 5

Internal problem ID [19425]
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. Misc. Exercise on chapter VII. Page 118
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:39:31 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(x),x$3)=sin(x)^2,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}]==Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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