Advertisements
Advertisements
प्रश्न
Find the differential equation representing the family of curves `y = ae^(bx + 5)`. where a and b are arbitrary constants.
Advertisements
उत्तर
Given : `y = ae^(bx + 5)`
Differentiating y with respect to x.
`(dy)/(dx) = ae^(bx + 5) (b) = be^(bx + 5) = by` (Since `y= ae^(bx + 5)`) .....1
Differentiating (1) again with respect to x we get
`(d^2y)/(dx^2) = b (dy)/(dx)` .....(2)
Dividing (2) by (1) we get
`((d^2y)/(dx^2))/(dy/dx) = (b(dy/dx))/(by)`
`=> y (d^2y)/(dx^2) = ((dy)/(dx))^2`
APPEARS IN
संबंधित प्रश्न
Write the integrating factor of the following differential equation:
(1+y2) dx−(tan−1 y−x) dy=0
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
`x/a + y/b = 1`
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = a e3x + b e– 2x
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = e2x (a + bx)
Find the particular solution of the differential equation (1 + e2x) dy + (1 + y2) ex dx = 0, given that y = 1 when x = 0.
Solve the differential equation `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`
Find a particular solution of the differential equation (x - y) (dx + dy) = dx - dy, given that y = -1, when x = 0. (Hint: put x - y = t)
The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is ______.
Form the differential equation having \[y = \left( \sin^{- 1} x \right)^2 + A \cos^{- 1} x + B\], where A and B are arbitrary constants, as its general solution.
The equation of the curve satisfying the differential equation y (x + y3) dx = x (y3 − x) dy and passing through the point (1, 1) is
Show that y2 − x2 − xy = a is a solution of the differential equation \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]
Show that the differential equation of all parabolas which have their axes parallel to y-axis is \[\frac{d^3 y}{d x^3} = 0.\]
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
\[\frac{dy}{dx} = x^2 e^x\]
\[(\tan^2 x + 2\tan x + 5)\frac{dy}{dx} = 2(1+\tan x)\sec^2x\]
tan y dx + tan x dy = 0
x cos2 y dx = y cos2 x dy
(1 − x2) dy + xy dx = xy2 dx
Find the general solution of the differential equation `"dy"/"dx" = y/x`.
Solve the differential equation:
cosec3 x dy − cosec y dx = 0
The general solution of the differential equation `(dy)/(dx) + x/y` = 0 is
If n is any integer, then the general solution of the equation `cos x - sin x = 1/sqrt(2)` is
The number of arbitrary constant in the general solution of a differential equation of fourth order are
Which of the following equations has `y = c_1e^x + c_2e^-x` as the general solution?
The general solution of the differential equation of the type `(dx)/(dy) + p_1y = theta_1` is
The general solution of the differential equation `(ydx - xdy)/y` = 0
Solve the differential equation: y dx + (x – y2)dy = 0
