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
Solve the differential equation `dy/dx=(y+sqrt(x^2+y^2))/x`
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 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 = x2 + 2x + C : y′ – 2x – 2 = 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 `dy/dx + y cot x = 4xcosec x(x != 0)`, given that y = 0 when `x = pi/2.`
Find a particular solution of the differential equation`(x + 1) dy/dx = 2e^(-y) - 1`, given that y = 0 when x = 0.
Solve the differential equation `cos^2 x dy/dx` + y = tan x
The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is
Solution of the differential equation \[\frac{dy}{dx} + \frac{y}{x}=\sin x\] 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
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
cos (x + y) dy = dx
\[\frac{dy}{dx} - y \tan x = - 2 \sin x\]
`y sec^2 x + (y + 7) tan x(dy)/(dx)=0`
\[\frac{dy}{dx} + y = 4x\]
\[\frac{dy}{dx} + 5y = \cos 4x\]
\[\cos^2 x\frac{dy}{dx} + y = \tan x\]
`x cos x(dy)/(dx)+y(x sin x + cos x)=1`
`2 cos x(dy)/(dx)+4y sin x = sin 2x," given that "y = 0" when "x = pi/3.`
Find the general solution of the differential equation \[\frac{dy}{dx} = \frac{x + 1}{2 - y}, y \neq 2\]
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:-
\[x\frac{dy}{dx} + 2y = x^2 , x \neq 0\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \frac{y}{x} = x^2\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \left( \sec x \right) y = \tan x\]
Solve the following differential equation:-
\[x \log x\frac{dy}{dx} + y = \frac{2}{x}\log x\]
The general solution of the differential equation x(1 + y2)dx + y(1 + x2)dy = 0 is (1 + x2)(1 + y2) = k.
If y(t) is a solution of `(1 + "t")"dy"/"dt" - "t"y` = 1 and y(0) = – 1, then show that y(1) = `-1/2`.
Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
The solution of `x ("d"y)/("d"x) + y` = ex is ______.
The solution of the equation (2y – 1)dx – (2x + 3)dy = 0 is ______.
The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx is ______.
The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is ______.
The member of arbitrary constants in the particulars solution of a differential equation of third order as
Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.
