Advertisements
Advertisements
प्रश्न
Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is ______.
विकल्प
cosx
tanx
secx
sinx
Advertisements
उत्तर
Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is secx.
Explanation:
The given differential equation is
`cos x * ("d"y)/("d"x) + y sinx` = 1
⇒ `("d"y)/("d"x) + sinx/cosx y = 1/cosx`
⇒ `("d"y)/("d"x) + tan x y = secx`
Here, P = tan x and Q = sec x
∴ Integrating factor = `"e"^(int Pdx)`
= `"e"^(int tan x "d"x)`
= `"e"^(log secx)`
= sec x.
APPEARS IN
संबंधित प्रश्न
Solve the differential equation cos(x +y) dy = dx hence find the particular solution for x = 0 and y = 0.
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = ex + 1 : y″ – y′ = 0
Find the general solution of the differential equation `dy/dx + sqrt((1-y^2)/(1-x^2)) = 0.`
Solve the differential equation `cos^2 x dy/dx` + y = tan x
Find the differential equation of the family of concentric circles `x^2 + y^2 = a^2`
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.
The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by
The solution of the differential equation \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], is
Find the general solution of the differential equation \[x \cos \left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x .\]
x (e2y − 1) dy + (x2 − 1) ey dx = 0
\[y - x\frac{dy}{dx} = b\left( 1 + x^2 \frac{dy}{dx} \right)\]
`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.
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sqrt{4 - y^2}, - 2 < y < 2\]
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:-
\[x \log x\frac{dy}{dx} + y = \frac{2}{x}\log x\]
Solve the following differential equation:-
(1 + x2) dy + 2xy dx = cot x dx
Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x2 + 1) dx, x ≠ 0.
Find the equation of a curve passing through the point (0, 0) and whose differential equation is \[\frac{dy}{dx} = e^x \sin x.\]
Find the differential equation of all non-horizontal lines in a plane.
Solution of the differential equation `"dx"/x + "dy"/y` = 0 is ______.
The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` 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 y2dx + (x2 – xy + y2) dy = 0.
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.
The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is ______.
The number of arbitrary constants in the general solution of a differential equation of order three is ______.
The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` is ______.
The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx2.
Which of the following differential equations has `y = x` as one of its particular solution?
Find a particular solution, satisfying the condition `(dy)/(dx) = y tan x ; y = 1` when `x = 0`
