Question

Determine whether the given differential equation is separable. StartFraction dy Over dx EndFraction plus 2 sine (x minus y )equals0 Is the differential equation​ separable?

Answer 1

Answer:

$dy/dx+2sin(x-y)=0$

so whether the given equation is separable or not

$dy/dx= -2sin(x-y)$

the given equation is not separable because the argument inside the function is dependent on both x and y

even though we use the formula to open the sin(A-B) we would still get the function dependent on both x and y and the equation would get complicated so instead use any other method.