60.1.6 problem 6

Internal problem ID [10020]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 6
Date solved : Wednesday, March 05, 2025 at 08:04:27 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \cos \left (x \right )-\frac {\sin \left (2 x \right )}{2}&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 15

ode:=diff(y(x),x)+y(x)*cos(x)-1/2*sin(2*x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 54

ode=D[y[x],x] + y[x]*Cos[x] - Sin[2*x]/2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x-\cos (K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}-\cos (K[1])dK[1]\right ) \cos (K[2]) \sin (K[2])dK[2]+c_1\right ) \]

✓ Sympy. Time used: 0.443 (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)
 

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