1.6 problem 6

Internal problem ID [8343]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 6.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

\[ \boxed {y^{\prime }+y \cos \left (x \right )=\frac {\sin \left (2 x \right )}{2}} \]

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 18

DSolve[y'[x] + y[x]*Cos[x] - Sin[2*x]/2==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

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