Q16 of 50 Page 193

Solve:

given:

To find: solution of the given differential equation

Re-writing the given equation as

It is clearly a homogenous differential equation

Assuming y=vx

Differentiating both sides

Substituting from the given equation

Now integrating both sides

Formula:

Substituting

is the solution of the given differential equation

Form the differential equation of all circles which pass through origin and whose centres lie on y-axis

Find the equation of a curve passing through origin and satisfying the differential equation

Find the general solution of the differential equation (1 + y²) + (x – e^tan–1y)

Find the general solution of y²dx + (x² – xy + y²) dy = 0.