Consider the differential equation: (y^2+2*x)dx+(2*x*y-1)dy = 0. (a) show that the equation is exact by evaluating (\partial m)/(\partial y) = (\partial n)/(\partial x)= (b) determine the general solution in implicit form: incorrect: your answer is incorrect. = c

The given ODE

is exact if . It so happens that we have , so it is indeed exact. For such an ODE, we're looking for a solution of the form , for which the differential is

so we have the following system of PDEs that allow us to solve for :

In the first PDE, we can integrate both sides with respect to and recover :

Then differentiating this with respect to returns :

So the general solution to the ODE is

or simply

answer: 34rtyj,jkhtyetwrhyjeuiejnbhdfknbkguxfrbhkfdbjvkmbd,kvbsd.kxjvbhjnfbgjxdfn

step-by-step explanation: