83.35.5 problem 5

Internal problem ID [19346]
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 : Thursday, March 13, 2025 at 02:16:36 PM
CAS classification : [[_3rd_order, _quadrature]]

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

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

ode:=diff(diff(diff(y(x),x),x),x) = sin(x)^2; 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=D[y[x],{x,3}]==Sin[x]^2; 
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: 0.464 (sec). Leaf size: 24

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

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