# What is the solution to the Differential Equation #dy/dx = sin(x+y) + cos(x+y)#?

##### 1 Answer

#### Explanation:

In it's present form this is not separable, but using the sine and cosine sum formula we have:

This is now separable (phew! But you do need to be good with trigonometry!), So "separating the variables" gives us:

The LHS integral is a real pig, This question is more about the separation process than horrific integration, so I will just quote the result which is:

So the solution is: