Advertisements
Advertisements
प्रश्न
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = cos x + C : y′ + sin x = 0
Advertisements
उत्तर
y = cos x + C
`dy/dx` = - sin x
⇒ y’ + sin x = 0
As a result, the function y = cos x + C provides a solution to the above differential equation.
APPEARS IN
संबंधित प्रश्न
If x = Φ(t) differentiable function of ‘ t ' then prove that `int f(x) dx=intf[phi(t)]phi'(t)dt`
Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
Find the general solution of the following differential equation :
`(1+y^2)+(x-e^(tan^(-1)y))dy/dx= 0`
The number of arbitrary constants in the general solution of a differential equation of fourth order are ______.
Find a particular solution of the differential equation`(x + 1) dy/dx = 2e^(-y) - 1`, given that y = 0 when x = 0.
Find the differential equation of the family of concentric circles `x^2 + y^2 = a^2`
The population of a town grows at the rate of 10% per year. Using differential equation, find how long will it take for the population to grow 4 times.
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
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 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
Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .
The solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x} + \frac{\phi\left( \frac{y}{x} \right)}{\phi'\left( \frac{y}{x} \right)}\] is
\[\frac{dy}{dx} - y \tan x = e^x \sec x\]
\[\frac{dy}{dx} - y \tan x = e^x\]
\[\frac{dy}{dx} + 2y = \sin 3x\]
\[\frac{dy}{dx} + y = 4x\]
Find the general solution of the differential equation \[\frac{dy}{dx} = \frac{x + 1}{2 - y}, y \neq 2\]
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sin^{- 1} x\]
Solve the following differential equation:-
\[x \log x\frac{dy}{dx} + y = \frac{2}{x}\log x\]
Solve the differential equation : `("x"^2 + 3"xy" + "y"^2)d"x" - "x"^2 d"y" = 0 "given that" "y" = 0 "when" "x" = 1`.
The general solution of the differential equation x(1 + y2)dx + y(1 + x2)dy = 0 is (1 + x2)(1 + y2) = k.
Find the general solution of `"dy"/"dx" + "a"y` = emx
Find the general solution of `(x + 2y^3) "dy"/"dx"` = y
Form the differential equation having y = (sin–1x)2 + Acos–1x + B, where A and B are arbitrary constants, as its general solution.
Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.
Find the general solution of (1 + tany)(dx – dy) + 2xdy = 0.
Find the general solution of `("d"y)/("d"x) -3y = sin2x`
tan–1x + tan–1y = c is the general solution of the differential equation ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.
Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.
The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.
Which of the following differential equations has `y = x` as one of its particular solution?
