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 particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0.
Solve the differential equation `dy/dx -y =e^x`
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)`
Find the general solution of the differential equation `dy/dx + sqrt((1-y^2)/(1-x^2)) = 0.`
If y = etan x+ (log x)tan x then find dy/dx
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 the differential equation (x2 + 1) \[\frac{dy}{dx}\] + (y2 + 1) = 0, is
The number of arbitrary constants in the particular solution of a differential equation of third order is
Find the particular solution of the differential equation `(1+y^2)+(x-e^(tan-1 )y)dy/dx=` given that y = 0 when x = 1.
\[\frac{dy}{dx} + \frac{y}{x} = \frac{y^2}{x^2}\]
(1 + y + x2 y) dx + (x + x3) dy = 0
\[\frac{dy}{dx} + 2y = \sin 3x\]
\[\cos^2 x\frac{dy}{dx} + y = \tan x\]
\[\left( 1 + y^2 \right) + \left( x - e^{- \tan^{- 1} y} \right)\frac{dy}{dx} = 0\]
\[y^2 + \left( x + \frac{1}{y} \right)\frac{dy}{dx} = 0\]
Solve the following differential equation:- \[\left( x - y \right)\frac{dy}{dx} = x + 2y\]
Solve the differential equation: ` ("x" + 1) (d"y")/(d"x") = 2e^-"y" - 1; y(0) = 0.`
Find the differential equation of all non-horizontal lines in a plane.
The solution of the differential equation `x "dt"/"dx" + 2y` = x2 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" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.
Find the general solution of `(x + 2y^3) "dy"/"dx"` = y
If y(x) is a solution of `((2 + sinx)/(1 + y))"dy"/"dx"` = – cosx and y (0) = 1, then find the value of `y(pi/2)`.
Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
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 general solution of ex cosy dx – ex siny dy = 0 is ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The differential equation for which y = acosx + bsinx is a solution, is ______.
Which of the following is the general solution of `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + y` = 0?
The solution of the differential equation `("d"y)/("d"x) + (2xy)/(1 + x^2) = 1/(1 + x^2)^2` is ______.
The solution of differential equation coty dx = xdy is ______.
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
Solve the differential equation:
`(xdy - ydx) ysin(y/x) = (ydx + xdy) xcos(y/x)`.
Find the particular solution satisfying the condition that y = π when x = 1.
