Question
Find the differential equation of the family of curves y = a sin (bx + c). a, b. c being arbitrary constants.
Solution
The given equation is
y = a sin (bx + c) ...(1)
Differentiating w.r.t.x, successively three times,
...(2)
...(3)
...(4)
From (1) and (2), (3) and (4), we get,
or
is the required differential equation.
y = a sin (bx + c) ...(1)
Differentiating w.r.t.x, successively three times,
...(2) ...(3) ...(4)From (1) and (2), (3) and (4), we get,
or
is the required differential equation.
