Advertisements
Advertisements
प्रश्न
The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` is ______.
Advertisements
उत्तर
The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` is `"e"^x . 1/x`.
Explanation:
The given differential equation is `("d"y)/("d"x) + y = (1 + y)/x`
⇒ `("d"y)/("d"x) + y = (1 + y)/x`
⇒ `("d"y)/("d"x) + y = 1/x + y/x`
⇒ `("d"y)/("d"x) + y - y/x = 1/x`
⇒ `("d"y)/("d"x) + (1 - 1/x) = 1/x`
Here P = `(1 - 1/x)`
∴ I.F. = `"e"^(intPdx)`
= `"e"^(int(1 - 1/x)"d"x)`
= `"e"^(x - logx)`
= `"e"^x . "e"^(-logx)`
= `"e"^x . "e"^(log 1/x)`
= `"e"^x . 1/x`
APPEARS IN
संबंधित प्रश्न
Find the particular solution of the differential equation `e^xsqrt(1-y^2)dx+y/xdy=0` , given that y=1 when x=0
Find the general solution of the following differential equation :
`(1+y^2)+(x-e^(tan^(-1)y))dy/dx= 0`
Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0.
Show that the general solution of the differential equation `dy/dx + (y^2 + y +1)/(x^2 + x + 1) = 0` is given by (x + y + 1) = A (1 - x - y - 2xy), where A is parameter.
Solve the differential equation `[e^(-2sqrtx)/sqrtx - y/sqrtx] dx/dy = 1 (x != 0).`
Find `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`
The general solution of the differential equation \[\frac{dy}{dx} + y\] g' (x) = g (x) g' (x), where g (x) is a given function of x, is
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 \[\frac{dy}{dx} + 1 = e^{x + y}\], is
Solve the differential equation (x2 − yx2) dy + (y2 + x2y2) dx = 0, given that y = 1, when x = 1.
The solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x} + \frac{\phi\left( \frac{y}{x} \right)}{\phi'\left( \frac{y}{x} \right)}\] is
x (e2y − 1) dy + (x2 − 1) ey dx = 0
\[\frac{dy}{dx} = \frac{y\left( x - y \right)}{x\left( x + y \right)}\]
(x + y − 1) dy = (x + y) dx
\[\frac{dy}{dx} - y \tan x = e^x \sec x\]
(1 + y + x2 y) dx + (x + x3) dy = 0
`y sec^2 x + (y + 7) tan x(dy)/(dx)=0`
`x cos x(dy)/(dx)+y(x sin x + cos x)=1`
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 the general solution:- `y log y dx − x dy = 0`
Solve the following differential equation:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
Find the equation of a curve passing through the point (0, 0) and whose differential equation is \[\frac{dy}{dx} = e^x \sin x.\]
Solve the differential equation : `("x"^2 + 3"xy" + "y"^2)d"x" - "x"^2 d"y" = 0 "given that" "y" = 0 "when" "x" = 1`.
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.
Find the general solution of y2dx + (x2 – xy + y2) dy = 0.
Solve the differential equation dy = cosx(2 – y cosecx) dx given that y = 2 when x = `pi/2`
Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.
Solution of differential equation xdy – ydx = 0 represents : ______.
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.
The general solution of ex cosy dx – ex siny dy = 0 is ______.
y = aemx+ be–mx satisfies which of the following differential equation?
The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx 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 ydx + (x + xy)dy = 0 is ______.
The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx2.
Find the general solution of the differential equation:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
