Question

(𝟐𝒙𝒚 − 𝒚^ 𝟐 + 𝒚)𝒅𝒙 + (𝟑𝒙^𝟐 − 𝟒𝒙𝒚 + 𝟑𝒙)𝒅𝒚 = 𝟎

Answer 1

(2xy-y²+y)dx +(3x² +4xy+3x)dy=0

M(x, y)=2xy - y² +y;

N(x, y)=3x² + 4xy + 3x;

test for I(x, y)=C

dM/dy =2x-2y ....(i)

=dN/dx=3.[2 x^(2-1) ] -4y= 6x-4y ...(ii)

since (i) is not equal to (ii) equation is not exact

hence I(x, y)=C does not exist.