Find the particular solution of the differential equation given that when x = 1, y = π 4 A differential equation is shown: x cos(y/x) dy/dx = y cos(y/x) + x.

Q37 of 462 Page 23

Find the particular solution of the differential equation given that when x = 1, y = π/4

Consider the given equation

this is homogeneous equation,

Put y = vx

And

So,

cos v dv =

sin v = log x + c

…… (1)

Put x = 1, y = in eq.(1),

c =

now,

Solve each of the following initial value problems

,y(2) = x

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