Advertisements
Advertisements
प्रश्न
The number of solutions of `("d"y)/("d"x) = (y + 1)/(x - 1)` when y (1) = 2 is ______.
विकल्प
None
One
Two
Infinite
Advertisements
उत्तर
The number of solutions of `("d"y)/("d"x) = (y + 1)/(x - 1)` when y (1) = 2 is one.
Explanation:
The given differential equation is `("d"y)/("d"x) = (y + 1)/(x - 1)`
⇒ `("d"y)/(y + 1) = ("d"x)/(x - 1)`
Integrating both sides, we get
`int ("d"y)/(y + 1) = int ("d"x)/(x - 1)`
⇒ log(y + 1) = log(x – 1) + log c
⇒ log(y + 1) – log(x – 1) = log c
⇒ `log|(y + 1)/(x - 1)|` = log c
⇒ `(y + 1)/(x - 1)` = c
Put x = 1 and y = 2
⇒ `(2 + 1)/(1 - 1)` = c
∴ c = `oo`
∴ `(y +1)/(x - 1) = 1/0`
⇒ x – 1 = 0
⇒ x = 1.
APPEARS IN
संबंधित प्रश्न
Solve the differential equation cos(x +y) dy = dx hence find the particular solution for x = 0 and y = 0.
The solution of the differential equation dy/dx = sec x – y tan x is:
(A) y sec x = tan x + c
(B) y sec x + tan x = c
(C) sec x = y tan x + c
(D) sec x + y tan x = c
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " 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`
If y = P eax + Q ebx, show that
`(d^y)/(dx^2)=(a+b)dy/dx+aby=0`
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 = x2 + 2x + C : y′ – 2x – 2 = 0
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = x sin x : xy' = `y + x sqrt (x^2 - y^2)` (x ≠ 0 and x > y or x < -y)
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 `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`
Write the order of the differential equation associated with the primitive y = C1 + C2 ex + C3 e−2x + C4, where C1, C2, C3, C4 are arbitrary constants.
The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by
The solution of the differential equation (x2 + 1) \[\frac{dy}{dx}\] + (y2 + 1) = 0, is
Which of the following differential equations has y = x as one of its particular solution?
The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is
\[\frac{dy}{dx} = \left( x + y \right)^2\]
\[\frac{dy}{dx} = \frac{y\left( x - y \right)}{x\left( x + y \right)}\]
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
`y sec^2 x + (y + 7) tan x(dy)/(dx)=0`
\[\cos^2 x\frac{dy}{dx} + y = \tan x\]
`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`
For the following differential equation, find the general solution:- `y log y dx − x dy = 0`
Solve the following differential equation:- \[x \cos\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\]
Solve the following differential equation:- `y dx + x log (y)/(x)dy-2x dy=0`
Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x-coordinate and the product of the x-coordinate and y-coordinate of that point.
Solve the differential equation: ` ("x" + 1) (d"y")/(d"x") = 2e^-"y" - 1; y(0) = 0.`
The solution of the differential equation `x "dt"/"dx" + 2y` = x2 is ______.
The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.
Form the differential equation having y = (sin–1x)2 + Acos–1x + B, where A and B are arbitrary constants, as its general solution.
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.
Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.
Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.
The differential equation for which y = acosx + bsinx is a solution, is ______.
Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.
The number of arbitrary constants in the general solution of a differential equation of order three is ______.
Find a particular solution, satisfying the condition `(dy)/(dx) = y tan x ; y = 1` when `x = 0`
