Advertisements
Advertisements
प्रश्न
The solution of `x ("d"y)/("d"x) + y` = ex is ______.
पर्याय
y = `"e"^x/x + "k"/x`
y = xex + cx
y = xex + k
x = `"e"^y/y + "k"/y`
Advertisements
उत्तर
The solution of `x ("d"y)/("d"x) + y` = ex is y = `"e"^x/x + "k"/x`.
Explanation:
The given differential equation is `x ("d"y)/("d"x) + y = "e"^x`
⇒ `("d"y)/("d"x) + y/x = "e"^x/x`
Here P = `1/x` and Q = `"e"^x/x`
∴ Integrating factor I.F. = `"e"^(int 1/x "d"x)`
= `"e"^(log |x|)`
= x
So, the solution is `y xx "I"."F". = int "Q" xx "I"."F". "d"x + "k"`
⇒ `y xx x = int "e"^x/x xx x "d"x + "k"`
⇒ `y xx x = int "e"^x "d"x + "k"`
⇒ `y xx x = "e"^x + "k"`
∴ y = `"e"^x/x + "k"/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.
Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.
Solve : 3ex tanydx + (1 +ex) sec2 ydy = 0
Also, find the particular solution when x = 0 and y = π.
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
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)`
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
xy = log y + C : `y' = (y^2)/(1 - xy) (xy != 1)`
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y – cos y = x : (y sin y + cos y + x) y′ = y
Find a particular solution of the differential equation `dy/dx + y cot x = 4xcosec x(x != 0)`, given that y = 0 when `x = pi/2.`
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 x2 + y2 \[\frac{dy}{dx}\]= 4, is
The solution of the differential equation \[\frac{dy}{dx} - ky = 0, y\left( 0 \right) = 1\] approaches to zero when x → ∞, if
The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], 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.
Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .
\[\frac{dy}{dx} = \frac{\sin x + x \cos x}{y\left( 2 \log y + 1 \right)}\]
\[\frac{dy}{dx} + 1 = e^{x + y}\]
(x3 − 2y3) dx + 3x2 y dy = 0
x2 dy + (x2 − xy + y2) dx = 0
\[y - x\frac{dy}{dx} = b\left( 1 + x^2 \frac{dy}{dx} \right)\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \frac{1 - \cos x}{1 + \cos x}\]
For the following differential equation, find the general solution:- `y log y dx − x dy = 0`
Solve the following differential equation:- `y dx + x log (y)/(x)dy-2x dy=0`
Solve the following differential equation:-
\[\frac{dy}{dx} + 2y = \sin x\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \frac{y}{x} = x^2\]
Solve the differential equation : `("x"^2 + 3"xy" + "y"^2)d"x" - "x"^2 d"y" = 0 "given that" "y" = 0 "when" "x" = 1`.
x + y = tan–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.
Find the general solution of `"dy"/"dx" + "a"y` = emx
The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.
The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` is ______.
The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is ______.
General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.
General solution of `("d"y)/("d"x) + y` = sinx is ______.
The solution of `("d"y)/("d"x) = (y/x)^(1/3)` is `y^(2/3) - x^(2/3)` = c.
Find the particular solution of the following differential equation, given that y = 0 when x = `pi/4`.
`(dy)/(dx) + ycotx = 2/(1 + sinx)`
Which of the following differential equations has `y = x` as one of its particular solution?
Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
