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(1 point) Use the mixed partials check to see if the following differential equation is exact. If it is exact find a function F(I, y)

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(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(I, y) whose differential, dF(z, y) gives the differential equation. That is, level curves F(z, y) = C are solutions to the differential equation: dy -213 - 3y 2c - 12 First rewrite as M(z, y) dx + N(z, y) dy = 0 where M(I, y) = and N(z, y) = If the equation is not exact, enter not exact, otherwise enter in F"(I, y) as the solution of the differential equation here - C. (1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(I, y) whose differential, dF(I, y) is the left hand side of the differential equation. That is, level curves F(z, y) = C are solutions to the differential equation (3e sin(y) + ly)dz + (1z + 3e# cos(y))dy = 0 First, if this equation has the form M(x, y)dr + N(z, y)dy = 0: My(I, y) = , and NE (x, y) = If the equation is not exact, enter not exact, otherwise enter in F(x, y) here 1 point) The differential equation can be written in differential form: M(z, y) dr + N(z, y) dy = 0 where M(I, y) = and N(I, y) = The term M(x, y) dir + N(x, y) dy becomes an exact differential if the left hand side above is divided by y", Integrating that new equation, the solution of the differential equation is = C

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