Advertisements
Advertisements
प्रश्न
The general solution of ex cosy dx – ex siny dy = 0 is ______.
पर्याय
ex cosy = k
ex siny = k
ex = k cosy
ex = k siny
Advertisements
उत्तर
The general solution of ex cosy dx – ex siny dy = 0 is ex cosy = k.
Explanation:
The given differential equation is ex cosy dx – ex siny dy = 0
⇒ ex (cosy dx – siny dy) = 0
⇒ cosy dx – siny dy = 0 ......[∵ ex ≠ 0]
⇒ siny dy = cosy dx
⇒ `siny/cosy "d"y` = dx
Integrating both sides, we have
`int siny/cosy "d"y = int "d"x`
⇒ `-log|cosy| = x + log "k"`
⇒ `log 1/cosy - log "k"` = x
⇒ `log(1/("k" cosy))` = x
⇒ `1/("k" cosy)` = ex
⇒ `1/"k"` = ex cosy
⇒ ex cosy = c .....`["c" = 1/"k"]`
APPEARS IN
संबंधित प्रश्न
If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`
Solve : 3ex tanydx + (1 +ex) sec2 ydy = 0
Also, find the particular solution when x = 0 and y = π.
Find the differential equation representing the curve y = cx + c2.
Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.
Find the particular solution of the differential equation x (1 + y2) dx – y (1 + x2) dy = 0, given that y = 1 when x = 0.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = ex + 1 : y″ – y′ = 0
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = Ax : xy′ = y (x ≠ 0)
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
x + y = tan–1y : y2 y′ + y2 + 1 = 0
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 general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is
The solution of the differential equation \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], is
If m and n are the order and degree of the differential equation \[\left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\], then
The solution of the differential equation (x2 + 1) \[\frac{dy}{dx}\] + (y2 + 1) = 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 ex dy + (y ex + 2x) dx = 0 is
`(2ax+x^2)(dy)/(dx)=a^2+2ax`
(x3 − 2y3) dx + 3x2 y dy = 0
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
\[x\frac{dy}{dx} + 2y = x^2 , x \neq 0\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \left( \sec x \right) y = \tan x\]
Solve the following differential equation:-
y dx + (x − y2) dy = 0
Find the equation of a curve passing through the point (−2, 3), given that the slope of the tangent to the curve at any point (x, y) is `(2x)/y^2.`
Find the equation of a curve passing through the point (0, 0) and whose differential equation is \[\frac{dy}{dx} = e^x \sin x.\]
The solution of the differential equation `x "dt"/"dx" + 2y` = x2 is ______.
The general solution of the differential equation x(1 + y2)dx + y(1 + x2)dy = 0 is (1 + x2)(1 + y2) = k.
Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.
Solve the differential equation dy = cosx(2 – y cosecx) dx given that y = 2 when x = `pi/2`
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.
The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx is ______.
The number of arbitrary constants in the general solution of a differential equation of order three is ______.
General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.
The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.
The solution of the differential equation ydx + (x + xy)dy = 0 is ______.
General solution of `("d"y)/("d"x) + y` = sinx is ______.
The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
