Advertisements
Advertisements
प्रश्न
Find `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`
Advertisements
उत्तर
Consider the differential equation sin2y + cosxy = K
Differentiate the above differential equation with respect to x, to get the value of `(dy)/(dx)`
`=> d/dx (sin^2 y) + d/dx (cos xy) = d/(dx) (K)`

संबंधित प्रश्न
Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = ex + 1 : y″ – y′ = 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:
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 ______.
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`
Solve the differential equation:
`e^(x/y)(1-x/y) + (1 + e^(x/y)) dx/dy = 0` when x = 0, y = 1
The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is
If m and n are the order and degree of the differential equation \[\left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\], then
The solution of the differential equation \[\frac{dy}{dx} + 1 = e^{x + y}\], is
The solution of the differential equation x dx + y dy = x2 y dy − y2 x dx, is
Which of the following differential equations has y = x as one of its particular solution?
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
\[\frac{dy}{dx} + \frac{y}{x} = \frac{y^2}{x^2}\]
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 a particular solution satisfying the given condition:
\[x\left( x^2 - 1 \right)\frac{dy}{dx} = 1, y = 0\text{ when }x = 2\]
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
\[x\frac{dy}{dx} + 2y = x^2 , x \neq 0\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \frac{y}{x} = x^2\]
The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
The solution of `x ("d"y)/("d"x) + y` = ex is ______.
The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.
The solution of the equation (2y – 1)dx – (2x + 3)dy = 0 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 ______.
Which of the following differential equations has `y = x` as one of its particular solution?
Find a particular solution, satisfying the condition `(dy)/(dx) = y tan x ; y = 1` when `x = 0`
