80.4.6 problem 6

Internal problem ID [18486]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 31. Problems at page 85
Problem number : 6
Date solved : Monday, March 31, 2025 at 05:37:12 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x)+y(x)*cos(x) = 1/2*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (x \right )-1+{\mathrm e}^{-\sin \left (x \right )} c_1 \]

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 18

ode=D[y[x],x]+y[x]*Cos[x]==1/2*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sin (x)+c_1 e^{-\sin (x)}-1 \]

✓ Sympy. Time used: 0.461 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} e^{- \sin {\left (x \right )}} + \sin {\left (x \right )} - 1 \]