Advertisements
Advertisements
प्रश्न
The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx2.
पर्याय
True
False
उत्तर
This statement is True.
Explanation:
The given differential equation is `("d"y)/("d"x) = (x + 2y)/x`
⇒ `("d"y)/("d"x) = 1 + 2 y/x`
⇒ `("d"y)/("d"x) = (2y)/x` = 1
Here, P = `(-2)/x` and Q = 1
Integrating factor I.F. = `"e"^(int(-2)/x "d"x)`
= `"e"^(-2 log x)`
= `"e"^(log x^-2)`
= `1/x^2`
∴ Solution is `y xx "I"."F". = int "Q" xx "I"."F". "d"x + "c"`
⇒ `y xx 1/x^2 = int 1 xx 1/x^2 "d"x + "c"`
⇒ `y/x^2 = int 1/x^2 "d"x + "c"`
⇒ `y/x^2 = - 1/x + "c"`
⇒ y = `-x + "c"x^2`
⇒ y + x = cx2
APPEARS IN
संबंधित प्रश्न
Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = x sin x : xy' = `y + x sqrt (x^2 - y^2)` (x ≠ 0 and x > y or x < -y)
The number of arbitrary constants in the particular solution of a differential equation of third order are ______.
Find the particular solution of the differential equation
`tan x * (dy)/(dx) = 2x tan x + x^2 - y`; `(tan x != 0)` given that y = 0 when `x = pi/2`
The solution of x2 + y2 \[\frac{dy}{dx}\]= 4, is
The solution of the differential equation x dx + y dy = x2 y dy − y2 x dx, is
The solution of the differential equation \[\frac{dy}{dx} = \frac{x^2 + xy + y^2}{x^2}\], is
The number of arbitrary constants in the general solution of differential equation of fourth order is
\[\frac{dy}{dx} = \left( x + y \right)^2\]
cos (x + y) dy = dx
\[\frac{dy}{dx} + \frac{y}{x} = \frac{y^2}{x^2}\]
\[\frac{dy}{dx} + 2y = \sin 3x\]
\[\frac{dy}{dx} + y = 4x\]
\[\frac{dy}{dx} + 5y = \cos 4x\]
`2 cos x(dy)/(dx)+4y sin x = sin 2x," given that "y = 0" when "x = pi/3.`
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
Solve the following differential equation:-
\[x\frac{dy}{dx} + 2y = x^2 \log x\]
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
The general solution of the differential equation `"dy"/"dx" + y/x` = 1 is ______.
The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.
Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.
Solve: `2(y + 3) - xy "dy"/"dx"` = 0, given that y(1) = – 2.
Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.
The number of solutions of `("d"y)/("d"x) = (y + 1)/(x - 1)` when y (1) = 2 is ______.
The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.
The solution of `x ("d"y)/("d"x) + y` = ex is ______.
The solution of the equation (2y – 1)dx – (2x + 3)dy = 0 is ______.
General solution of `("d"y)/("d"x) + ytanx = secx` is ______.
The solution of the differential equation ydx + (x + xy)dy = 0 is ______.
