`(x^3+3x y^2)dx+(y^3+3x^2y)dy=0`

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

Solve: (x^(3)+3xy^(2))dx=(y^(3)-3x^(2)y)dy

(x^(3)-3xy^(2))dx=(y^(3)-3x^(2)y)dy

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

If y^(3) - 3y^(2) x=x^(3) +3x^(2) y,then (dy)/(dx)=

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

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as Solution of the differential equation (dy)/(dx)=e^(3x-2y)+x^2e^(-2y) is (e^(2y))/(2)=(e^(3x))/(3)+(x^2)/(2)+C Reason (R) : (dy)/(dx)=e^(3x-2y)+x^2e^(-2y) (dy)/(dx)=e^(-2y)(e^(3x)+x^2) separating the variables e^(2y)dy=(e^(3x)+x^2)dx int e^(2y)dy=int(e^(3x)+x^2)dx (e^(2y))/(2)=(e^(3x))/(3)+(x^3)/(3)+C .

Which of the following is a homogeneous differential equation? (A) (4x+6y+5)dy-(3y+2x+4)dx= (B) (xy)dx-(x^(3)+y^(3))dy=0 (C) quad y^(2)dx+(x^(2)-xy-y^(2))dy=0

Solve: (2x ^ (2) y ^ (2) + y) dx + (3x-x ^ (3) y) dy = 0

dy/dx =(y)/(2y^3+x)