Question

(xy^2)dx + (zx^2)dy −( x^2y^2)dz=0

Answer 1

Comparing the given differential equation with Pdx + Qdy +Rdz = 0, we get

P= xy²

Q= zx²

R= -x²y²

Now , we will first check if the given differential equation satisfies the condition of integrability which is given by

must be equal to zero.

here,

xy² ( x² + 2x²y ) + zx² (-2xy² ) - x²y² (2xy-2xz ) = x³y²-4x³y³ which is not equal to zero.

Hence, the given differential equation is not integrable.