Advertisements
Advertisements
Question
y = aemx+ be–mx satisfies which of the following differential equation?
Options
`("d"y)/("d"x) + "m"y` = 0
`("d"y)/("d"x) - "m"y` = 0
`("d"^2y)/("d"x^2) - "m"^2y` = 0
`("d"^2y)/("d"x^2) + "m"^2y` = 0
Solution
`("d"^2y)/("d"x^2) - "m"^2y` = 0
Explanation:
The given equation is y = `"ae"^("m"x) + "be"^(-"m"x)`
On differentiation, we get `("d"y)/("d"x) = "a" . "me"^("m"x) - "b" . "m"e^(-"m"x)`
Again differentiating w.r.t., we have
`("d"^2y)/("d"x^2) = "am"^2 "e"^("m"x) + "bm"^2 "e"^(-"m"x)`
⇒ `("d"^2y)/("d"x^2) = "m"^2 ("ae"^("m"x) + "be"^(-"m"x))`
⇒ `("d"^2y)/("d"x^2) = "m"^2y`
⇒ `("d"^2y)/("d"x^2) - "m"^2y` = 0
APPEARS IN
RELATED QUESTIONS
Find the particular solution of the differential equation `e^xsqrt(1-y^2)dx+y/xdy=0` , given that y=1 when x=0
Find the particular solution of the differential equation `(1+x^2)dy/dx=(e^(mtan^-1 x)-y)` , give that y=1 when x=0.
Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y – cos y = x : (y sin y + cos y + x) y′ = y
The population of a town grows at the rate of 10% per year. Using differential equation, find how long will it take for the population to grow 4 times.
Write the order of the differential equation associated with the primitive y = C1 + C2 ex + C3 e−2x + C4, where C1, C2, C3, C4 are arbitrary constants.
The solution of the differential equation \[\frac{dy}{dx} = \frac{x^2 + xy + y^2}{x^2}\], is
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is
Find the particular solution of the differential equation `(1+y^2)+(x-e^(tan-1 )y)dy/dx=` given that y = 0 when x = 1.
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
(x2 + 1) dy + (2y − 1) dx = 0
\[y^2 + \left( x + \frac{1}{y} \right)\frac{dy}{dx} = 0\]
Solve the differential equation:
(1 + y2) dx = (tan−1 y − x) dy
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \frac{1 - \cos x}{1 + \cos x}\]
For the following differential equation, find a particular solution satisfying the given condition:- \[\frac{dy}{dx} = y \tan x, y = 1\text{ when }x = 0\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \frac{y}{x} = x^2\]
Solve the following differential equation:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
Solve the differential equation: ` ("x" + 1) (d"y")/(d"x") = 2e^-"y" - 1; y(0) = 0.`
Solve the differential equation : `("x"^2 + 3"xy" + "y"^2)d"x" - "x"^2 d"y" = 0 "given that" "y" = 0 "when" "x" = 1`.
Find the general solution of y2dx + (x2 – xy + y2) dy = 0.
Solution of differential equation xdy – ydx = 0 represents : ______.
The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` is ______.
The solution of the differential equation ydx + (x + xy)dy = 0 is ______.
The solution of differential equation coty dx = xdy is ______.
The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` is ______.
Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0
Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.
