Advertisements
Advertisements
प्रश्न
The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is ______.
पर्याय
`("d"^2y)/("d"x^2) - alpha^2y` = 0
`("d"^2y)/("d"x^2) + alpha^2y` = 0
`("d"^2y)/("d"x^2) + alphay` = 0
`("d"^2y)/("d"x^2) - alphay` = 0
उत्तर
The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is `("d"^2y)/("d"x^2) + alpha^2y` = 0.
Explanation:
Given equation is : y = A cos a x + B sin a x
Differentiating both sides w.r.t. x, we have
`("d"y)/("d"x) = -"A" sin alpha x * alpha + "B" cos alpha x * alpha`
= `- "A" alpha sin alphax + "B" alpha cos alpha x`
Again differentiating w.r.t. x, we get
`("d"^2y)/("d"x^2) = -"A"alpha^2 cos alpha x - "B" alpha^2 sin alpha x`
⇒ `("d"^2y)/("d"x^2) = -alpha^2 ("A" cos alphax + "B" sin alpha x)`
⇒ `("d"^2y)/("d"x^2) = - alpha^2y`
⇒ `("d"^2y)/("d"x^2) + alpha^2y` = 0
APPEARS IN
संबंधित प्रश्न
The differential equation of `y=c/x+c^2` is :
(a)`x^4(dy/dx)^2-xdy/dx=y`
(b)`(d^2y)/dx^2+xdy/dx+y=0`
(c)`x^3(dy/dx)^2+xdy/dx=y`
(d)`(d^2y)/dx^2+dy/dx-y=0`
Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
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
Solve the differential equation `[e^(-2sqrtx)/sqrtx - y/sqrtx] dx/dy = 1 (x != 0).`
Solve the differential equation:
`e^(x/y)(1-x/y) + (1 + e^(x/y)) dx/dy = 0` when x = 0, y = 1
The solution of the differential equation \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is
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 \[\frac{y dx - x dy}{y} = 0\], is
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\] given that
\[\frac{dy}{dx} = \frac{\sin x + x \cos x}{y\left( 2 \log y + 1 \right)}\]
cos (x + y) dy = dx
(x + y − 1) dy = (x + y) dx
x2 dy + (x2 − xy + y2) dx = 0
\[y^2 + \left( x + \frac{1}{y} \right)\frac{dy}{dx} = 0\]
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \frac{1 - \cos x}{1 + \cos x}\]
Solve the following differential equation:-
\[\frac{dy}{dx} + 2y = \sin x\]
Find a particular solution of the following differential equation:- x2 dy + (xy + y2) dx = 0; y = 1 when x = 1
Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x-coordinate and the product of the x-coordinate and y-coordinate of that point.
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
Solve: `y + "d"/("d"x) (xy) = x(sinx + logx)`
Find the general solution of `("d"y)/("d"x) -3y = sin2x`
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.
The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx2.
Solve the differential equation:
`(xdy - ydx) ysin(y/x) = (ydx + xdy) xcos(y/x)`.
Find the particular solution satisfying the condition that y = π when x = 1.
