Question

Determine the equation of the curve passing through the origin in the form y = f(x) which satisfies the differential equation dy/dx = sin(10x + 6y).

Answer 1

The given differential equation is

dy/dx = sin(10x + 6y) ...(i)

Let 10x + 6y = v

10 + 6(dy/dx) = dv/dx

dy/dx = (1/6)((dv/dx) – 10)

(Let tan(v/2) = t)

which is passing through origin so c = (1/4)tan^–1(3/4).

Thus, the equation of the curve is

(1/4)tan^–1((5tan(5x + 3y) + 3)/4) = x + (1/4)tan^–1(3/4)