22. Solve (e^x+e^{-x})dy/dx=y^2 be separable method

To solve the differential equation by separable method, we need to rearrange it so that all the terms are on one side and all the terms are on the other side. Then, we can integrate both sides to obtain the solution.

First, we can multiply both sides by and divide both sides by to get:

Now, we can integrate both sides with respect to their respective variables:

To integrate the left-hand side, we can use the power rule:

where is constant of integration.

To integrate the right-hand side, we can use the substitution and , which gives us:

where is another constant of integration.

Substituting back into the equation and simplifying, we get:

Multiplying both sides by , we get:

Therefore, the general solution to the differential equation is:

where is an arbitrary constant of integration.