Advertisements
Advertisements
प्रश्न
The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` is ______.
पर्याय
`"e"^(x^2 - y)` = c
`"e"^-y + "e"^(x^2)` = c
`"e"^-y = "e"^(x^2)` + c
`"e"^(x^2 + y)` = c
Advertisements
उत्तर
The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` is `"e"^-y = "e"^(x^2)` + c.
Explanation:
The given differential equation is `("d"y)/("d"x) = 2x"e"^(x^2 - y)`
⇒ `("d"y)/("d"x) = 2x . "e"^(x^2) . "e"^-y`
⇒ `("d"y)/("e"^-y) = 2x . "e"^(x^2) "d"x`
Integrating both sides, we have
`int ("d"y)/("e"^-y) = int 2x . "e"^(x^2) "d"x`
⇒ `int "e"^y "d"y = int 2x . "e"^(x^2) "d"x`
Pit in R.H.S. x2 = t
∴ 2x dx = dt
∴ `int "e"^y "d"y = int "e"^"t" "dt"`
⇒ ey = et + c
⇒ ey = `"e"^(y^2) + "c"`
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
If y = P eax + Q ebx, show that
`(d^y)/(dx^2)=(a+b)dy/dx+aby=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:
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
The number of arbitrary constants in the general solution of a differential equation of fourth order are ______.
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.
Find a particular solution of the differential equation`(x + 1) dy/dx = 2e^(-y) - 1`, given that y = 0 when x = 0.
How many arbitrary constants are there in the general solution of the differential equation of order 3.
The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents
The solution of the differential equation x dx + y dy = x2 y dy − y2 x dx, is
The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is
The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\] given that
x (e2y − 1) dy + (x2 − 1) ey dx = 0
\[\frac{dy}{dx} + 1 = e^{x + y}\]
(1 + y + x2 y) dx + (x + x3) dy = 0
(x2 + 1) dy + (2y − 1) dx = 0
\[\cos^2 x\frac{dy}{dx} + y = \tan x\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \left( 1 + x^2 \right)\left( 1 + y^2 \right)\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} + y = 1\]
For the following differential equation, find a particular solution satisfying the given condition:
\[x\left( x^2 - 1 \right)\frac{dy}{dx} = 1, y = 0\text{ when }x = 2\]
For the following differential equation, find a particular solution satisfying the given condition:- \[\frac{dy}{dx} = y \tan x, y = 1\text{ when }x = 0\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \left( \sec x \right) y = \tan x\]
Solve the following differential equation:-
\[x \log x\frac{dy}{dx} + y = \frac{2}{x}\log x\]
Solve the following differential equation:-
\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]
Find the general solution of `"dy"/"dx" + "a"y` = emx
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 (1 + tany)(dx – dy) + 2xdy = 0.
Solution of differential equation xdy – ydx = 0 represents : ______.
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.
The solution of the differential equation `("d"y)/("d"x) + (2xy)/(1 + x^2) = 1/(1 + x^2)^2` is ______.
General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
Find the general solution of the differential equation:
`log((dy)/(dx)) = ax + by`.
