To solve this differential equation, we will first rearrange the terms and then apply the method of separation of variables.

Given equation: (1 x^2)y'=(e^mtan-1x-- y)

Rearranging the terms, we have:

y' = (e^mtan-1x-- y) / (1 x^2)

Now, let's separate the variables by multiplying both sides of the equation by (1 x^2):

(1 x^2)dy = (e^mtan-1x-- y)dx

Next, we will integrate both sides of the equation:

∫(1 x^2)dy = ∫(e^mtan-1x-- y)dx

Integrating the left-hand side gives:

∫(1 x^2)dy = y/x + C1

where C1 is the constant of integration.

Integrating the right-hand side requires a substitution. Let u = tan^(-1)(x), then du = (1/1+x^2)dx. The equation becomes:

∫(e^m u - y)du = ∫(e^m tan-1x - y)dx

Applying the substitution, we have:

∫(e^m u - y)du = ∫e^m tan-1x dx

∫(e^m u - y)du = ∫e^m u du

Integrating both sides gives:

(e^m u - y) = (1/m)e^m u + C2

where C2 is another constant of integration.

Now, let's solve for y:

e^m u - y = (1/m)e^m u + C2

y = e^m u - (1/m)e^m u - C2

Substituting back u = tan^(-1)(x), we get:

y = e^m tan-1x - (1/m)e^m tan-1x - C2

Therefore, the solution to the differential equation is:

y = (e^m - 1/m)e^m tan-1x - C2

where C2 is an arbitrary constant.