1.

The differential equation obtained by eliminating a and b from `y = ae^(bx)` isA. `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» Correct Answer - c
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


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