Question

Are the differential equations below separable dy/dx=-cos(x y)

Answer 1

Yes, the given differential equation dy/dx = -cos(xy) is separable. To solve separable differential equations, we need to separate the variables and integrate each side. The solution to the given differential equation is y = -sin(xy) + C.

Step-by-step explanation:

Yes, the given differential equation dy/dx = -cos(xy) is separable.

To solve separable differential equations, we need to separate the variables and integrate each side.

In this case, we can rewrite the equation as dy = -cos(xy)dx.

Now, we can integrate both sides of the equation separately:

∫dy = -∫cos(xy)dx.

After integrating, we get y = -sin(xy) + C, where C is the constant of integration.

Therefore, the solution to the given differential equation is y = -sin(xy) + C.