Q6 of 118 Page 419

Find the general solution of the differential equation

It is given that

On integrating, we get,

⇒ sin^-1x + sin^-1y = C

Prove that x² – y² = c (x² + y²)² is the general solution of differential equation (x³–3xy²) dx = (y³–3x²y)dy, where c is a parameter.

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

Show that the general solution of the differential equation is given by (x + y + 1) = A (1 – x – y – 2xy), where A is parameter.

Find the equation of the curve passing through the point whose differential equation is sin x cos y dx + cos x sin y dy = 0.