The differential equation obtained by eliminating a and b from `y = ae^(bx)` is

Options

A. `y(d^(2)y)/(dx^(2))+(dy)/(dx)=0`
B. ` y (d^(2)y)/(dx^(2))-(dy)/(dx)=0`
C. `y(d^(2)y)/(dx^(2))-((dy)/(dx))^(2)=0`
D. ` y (d^(2)y)/(dx^(2))+((dy)/(dx))^(2)=0`

Answer

c

Explanation

The given equation is
` y=ae^(bx)" "` …(i)
On differentiating w.r.t. x, we get
`(dy)/(dx)= abe^(bx)`
Again , on differentiating w.r.t x, we get
` (d^(2)y)/(dx^(2)) = ab^(2)e^(bx) rArr ae^(bx) (d^(2)y)/(dx^(2)) = a^(2)b^(2)e^(2bx)`
` rArr y (d^(2)y)/(dx^(2)) = (dy/(dx))^(2) rArr y (d^(2)y)/(dx^(2)) - (dy/dx)^(2)=0`
which is required differential equation