Question

Solve the differential equation

cos²(x – 2y) = `1 - 2dy/dx`

Answer 1

cos²(x – 2y) = `1 - (2dy)/dx`

Put x – 2y = v

∴ `(1 - (2dy)/dx) = (dv)/dx`

∴ Given equation becomes

cos²v = `(dv)/dx`

∴ dx = sec²v dv

∴ `int dx = int sec^2v  dv`

∴ x = tan v + c

∴ x = tan (x – 2y) + c