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Evaluate:

x²y dx – (x³ + y³)dy = 0
Evaluate:

Form the differential equation representing the family of curves y = A cos (x + B), where A and B are constants.
Evaluate:

(3xy + y²) dx + (x²+ xy) dy = 0
Evaluate:

Evaluate:

Evaluate:

Form the differential equation of the family of circles in the second quadrant and touching the coordinate
axes.
Form the differential equation of the family of parabolas having vertex at the origin and axis along positive y-axis.
Find the particular solution of the differential equation.

ex tan y dx + (1 – ex) sec2y dy=0
Form the differential equation of the family of circles touching the y-axis at origin.