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 differential equation representing the curve y = cx + c2.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
`y sqrt(1 + x^2) : y' = (xy)/(1+x^2)`
The number of arbitrary constants in the particular solution of a differential equation of third order are ______.
Solve the differential equation `[e^(-2sqrtx)/sqrtx - y/sqrtx] dx/dy = 1 (x != 0).`
If y = etan x+ (log x)tan x then find dy/dx
Solve the differential equation `cos^2 x dy/dx` + y = tan x
if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`
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 \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by
The solution of the differential equation \[\frac{dy}{dx} + 1 = e^{x + y}\], is
The solution of the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + 1 + y^2 = 0\], is
The number of arbitrary constants in the general solution of differential equation of fourth order is
The number of arbitrary constants in the particular solution of a differential equation of third order is
Which of the following differential equations has y = x as one of its particular solution?
(x + y − 1) dy = (x + y) dx
\[\frac{dy}{dx} - y \tan x = e^x \sec x\]
`y sec^2 x + (y + 7) tan x(dy)/(dx)=0`
`(2ax+x^2)(dy)/(dx)=a^2+2ax`
\[y^2 + \left( x + \frac{1}{y} \right)\frac{dy}{dx} = 0\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \frac{1 - \cos x}{1 + \cos x}\]
Solve the following differential equation:- \[x \cos\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\]
Solve the following differential equation:- `y dx + x log (y)/(x)dy-2x dy=0`
Solve the following differential equation:-
\[\frac{dy}{dx} + \frac{y}{x} = x^2\]
x + y = tan–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.
y = x is a particular solution of the differential equation `("d"^2y)/("d"x^2) - x^2 "dy"/"dx" + xy` = x.
Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.
The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is ______.
Solution of differential equation xdy – ydx = 0 represents : ______.
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.
General solution of `("d"y)/("d"x) + ytanx = secx` is ______.
Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0
If the solution curve of the differential equation `(dy)/(dx) = (x + y - 2)/(x - y)` passes through the point (2, 1) and (k + 1, 2), k > 0, then ______.
