Advertisements
Advertisements
प्रश्न
If y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`
Advertisements
उत्तर
y=2 cos(logx)+3 sin(logx)
Differentiating both sides with respect to x, we get
`dy/dx=2xxd/dx cos(logx)+3xx d/dxsin(log x)`
`=-2sin(logx)xx1/x+3 cos(logx)xx1/x`
`=>x dy/dx=-2 sin(logx)+3 cos(logx)`
Again, differentiating both sides with respect to x, we get
`x (d^2y)/(dx^2)+dy/dx=-2cos(logx)xx1/x-3 sin(logx)xx1/x`
`x^2 (d^2y)/(dx^2)+xdy/dx=-[2 cos(logx)+3sin(logx)]`
`x^2 (d^2y)/(dx^2)+xdy/dx=-y`
`x^2 (d^2y)/(dx^2)+xdy/dx+y=0`
APPEARS IN
संबंधित प्रश्न
Find the second order derivative of the function.
log x
Find the second order derivative of the function.
x3 log x
Find the second order derivative of the function.
ex sin 5x
Find the second order derivative of the function.
log (log x)
Find the second order derivative of the function.
sin (log x)
If y = 5 cos x – 3 sin x, prove that `(d^2y)/(dx^2) + y = 0`.
If y = 500e7x + 600e–7x, show that `(d^2y)/(dx^2)` = 49y.
If `x^3y^5 = (x + y)^8` , then show that `(dy)/(dx) = y/x`
Find `("d"^2"y")/"dx"^2`, if y = `"x"^5`
Find `("d"^2"y")/"dx"^2`, if y = `"x"^-7`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"log x"`
Find `("d"^2"y")/"dx"^2`, if y = log (x).
Find `("d"^2"y")/"dx"^2`, if y = 2at, x = at2
Find `("d"^2"y")/"dx"^2`, if y = `"x"^2 * "e"^"x"`
sec(x + y) = xy
If x2 + y2 + sin y = 4, then the value of `(d^2y)/(dx^2)` at the point (–2, 0) is ______.
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.
Read the following passage and answer the questions given below:
|
The relation between the height of the plant ('y' in cm) with respect to its exposure to the sunlight is governed by the following equation y = `4x - 1/2 x^2`, where 'x' is the number of days exposed to the sunlight, for x ≤ 3.
|
- Find the rate of growth of the plant with respect to the number of days exposed to the sunlight.
- Does the rate of growth of the plant increase or decrease in the first three days? What will be the height of the plant after 2 days?
Find `(d^2y)/dx^2 if, y = e^((2x + 1))`
Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`
Find `(d^2y)/dx^2` if, y = `e^(2x +1)`
Find `(d^2y)/dx^2, "if" y = e^((2x+1))`
Higher order derivatives are obtained by which process?
For \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\], what is \[\frac{d^2y}{dx^2}\]?
Which equation is equivalent to \[\frac{dy}{dx}=\frac{1}{\sqrt{1-x^2}}\] for \[y=\sin^{-1}x\]?
What is \[\frac{d}{dx}\left(\sqrt{1-x^2}\right)\] in the differentiation for \[y=\sin^{-1}x\]?
What equation is obtained after multiplying through by \[\sqrt{1-x^2}\] in the derivation for \[y=\sin^{-1}x\]?
Differentiating \[(1-x^2)y_{1}^{2}=1\] gives which expression?
Which equation follows from \[(1-x^2)\cdot2y_{1}y_{2}+y_{1}^{2}(0-2x)=0\]?
