Consider, pls, this option.
Put the equation in standard linear form.

Find the integrating factor.

Multiply both sides by
.

Now the left side the derivative of a product,

Integrate both sides.

On the right side, integrate by parts.

Solve for
.

Answer:
Step-by-step explanation:
This is what I got
I'm taking the liberty of editing your function as follows: <span>w=4r^2+6s^2, where I use " ^ " to indicate exponentiation.
The partial of w with respect to r is 8r. That with respect to s is 12s.</span>