Question
Form the differential equation of the family of curves by eliminating arbitrary constants a and b.
y = ex (a cosx + b sinx)
Solution
The given equation is
y = ex (a cosx + b sinx) ...(1)
Differentiating both sides w.r.t x, we get
or
...(2)
Again differentiating w.r.t x,
or
or
or
, which is required differential equation.
y = ex (a cosx + b sinx) ...(1)
Differentiating both sides w.r.t x, we get
or
...(2)Again differentiating w.r.t x,
or
or
or
, which is required differential equation.
