Question

(1 point) Use the \"mixed partials\" check to see if the following differential equation is exact. If it is exact find a function $F(x, y)$ whose differential, $dF(x, y)$ is the left hand side of the differential equation. That is, level curves $F(x, y) = C$ are solutions to the differential equation $(1xy^2 - 2y)dx + (1x^2y - 4x)dy = 0$ First: $M_y(x, y) = 2xy - 2$ and $N_x(x, y) = 2xy - 4$ if the equation is not exact, enter not exact, otherwise enter in $F(x, y)$ here $1/2y^2x^2 - 2yx$

          (1 point) Use the \"mixed partials\" check to see if the following differential equation is exact.
If it is exact find a function $F(x, y)$ whose differential, $dF(x, y)$ is the left hand side of the differential equation. That is, level curves $F(x, y) = C$ are solutions to the differential equation
$(1xy^2 - 2y)dx + (1x^2y - 4x)dy = 0$
First:
$M_y(x, y) = 2xy - 2$
and $N_x(x, y) = 2xy - 4$
if the equation is not exact, enter not exact, otherwise enter in $F(x, y)$ here $1/2y^2x^2 - 2yx$

(1 point) Use the m̈ixed partialsc̈heck to see if the following differential equation is exact.
If it is exact find a function F(x, y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation
(1xy^2 - 2y)dx + (1x^2y - 4x)dy = 0
First:
My(x, y) = 2xy - 2
and Nx(x, y) = 2xy - 4
if the equation is not exact, enter not exact, otherwise enter in F(x, y) here 1/2y^2x^2 - 2yx

Added by Patricia P.

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