Advertisements
Advertisements
प्रश्न
If y = sin (sin x), prove that `(d^2y)/(dx^2) + tan x dy/dx + y cos^2 x = 0`
Advertisements
उत्तर
y = sin(sin x)
`dy/dx = cos(sin x).cos x`
`(d^2y)/(dx^2) = cos (sin x).(-sinx) + cosx {-sin(sinx)}.cos x = - sin x.cos(sin x) - y cos^2 x`
Now
`(d^2y)/(dx^2) + tanx . (dy)/(dx) + ycos^2 x`
`= -sin x. cos (sin x) - ycos^2x + sinx/cosx.cos(sin x).cosx + ycos^2x`
`= -sinx.cos(sinx) - ycos^2x + sin x.cos(sin x) + ycos^2x`
= 0
Hence proved
APPEARS IN
संबंधित प्रश्न
If x = sin t, y = sin pt, prove that`(1-"x"^2)("d"^2"y")/"dx"^2 - "x" "dy"/"dx" + "p"^2"y" = 0`
If [x] stands for the integral part of x, then ____________.
| The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation y = 4x - `1/2 x^2` where x is the number of days exposed to sunlight. |  |
The rate of growth of the plant with respect to sunlight is ______.
| The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation y = 4x - `1/2 x^2` where x is the number of days exposed to sunlight. | |
What is the number of days it will take for the plant to grow to the maximum height?
| The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation y = 4x - `1/2 x^2` where x is the number of days exposed to sunlight. | |
What is the maximum height of the plant?
| The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation y = 4x - `1/2 x^2` where x is the number of days exposed to sunlight. | |
What will be the height of the plant after 2 days?
| The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation y = 4x - `1/2 x^2` where x is the number of days exposed to sunlight. | |
If the height of the plant is 7/2 cm, the number of days it has been exposed to the sunlight is ______.
