dz =(−sinx + 2xy^2)dx +(2x^2 y)dy

Question

Integrate the differential to find the function z.

Would I say that z was equal to two separate differentials and integrate the first part of the function with respect to x and the second part with respect to y?
z = cosx + x^2 y^2 + x^2 y^2 + C
z = cosx + 2(x^2 y^2) + C

Is this right or have I gone wrong?

Answer 1

you can check..

If z=cosx + 2x^2y^2 + C
then dz/dx= -sinx + 4xy^2 + 4x^2y dy/dx
which is not exactly what you started with.
check my thinking.