Show that the family of curves for which is given by Two mathematical equations are shown. The first is a differential equation: dy/dx = (x^2 + y^2) / (2xy). The second equation is x^2 - y^2 = Cx.

Q40 of 462 Page 23

Show that the family of curves for which is given by

Here,

C = …… (i)

Differentiate both side,

2x dx – C dx = 2y dy

…… (ii)

Put equation (i) in equation(ii),We get,

Hence prove.

Find the particular solution of the differential equation given that when x = 1, y = 0

Find the particular solution of the differential equation given that when y = 1, x = 0

Solve the following differential equations :