Advertisements
Advertisements
प्रश्न
Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.
पर्याय
x(y + cosx) = sinx + c
x(y – cosx) = sinx + c
xy cosx = sinx + c
x(y + cosx) = cosx + c
Advertisements
उत्तर
Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is x(y + cosx) = sinx + c.
Explanation:
The given differential equation is `("d"y)/("d"x) + y/x` = sec x
Since, it is a linear differential equation
∴ P = `1/x` and Q = sin x
Integrating factor I.F. = `"e"^(int 1/x "d"x)`
= `"e"^(log x)`
= x
∴ Solution is `y xx "I"."F" = int "Q" xx "I"."F". "d"x + "c"`
`y xx x = int sinx . x "d"x + "c"`
⇒ `y xx x = int x sin x "d"x + "c"`
⇒ `yx = x . int sinx "d"x - int("D"(x)intsinx "d"x)"d"x + "c"`
⇒ `yx = x(- cos x) - int - cos x "d"x`
⇒ `yx = - x cosx + int cosx "d"x`
⇒ `yx = -x cosx + sinx + "c"`
⇒ `yx + cosx = sinx + "c"`
⇒ `x(y + cosx) = sinx + "c"`
APPEARS IN
संबंधित प्रश्न
Solve the differential equation `dy/dx=(y+sqrt(x^2+y^2))/x`
Find the differential equation representing the curve y = cx + c2.
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 `dy/dx=(xy)/(x^2+y^2)` 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`
Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
`y sqrt(1 + x^2) : y' = (xy)/(1+x^2)`
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = Ax : xy′ = y (x ≠ 0)
The number of arbitrary constants in the particular solution of a differential equation of third 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`
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 \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], 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 \[\frac{dy}{dx} = \frac{y}{x} + \frac{\phi\left( \frac{y}{x} \right)}{\phi'\left( \frac{y}{x} \right)}\] is
\[\frac{dy}{dx} = \left( x + y \right)^2\]
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
\[\frac{dy}{dx} - y \tan x = - 2 \sin x\]
\[\frac{dy}{dx} + y = 4x\]
\[y^2 + \left( x + \frac{1}{y} \right)\frac{dy}{dx} = 0\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sqrt{4 - y^2}, - 2 < y < 2\]
For the following differential equation, find the general solution:- `y log y dx − x dy = 0`
For the following differential equation, find the general solution:- \[\frac{dy}{dx} + y = 1\]
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \frac{y}{x} = x^2\]
Solve the following differential equation:-
\[x\frac{dy}{dx} + 2y = x^2 \log x\]
Solve the differential equation: `(d"y")/(d"x") - (2"x")/(1+"x"^2) "y" = "x"^2 + 2`
The solution of the differential equation `x "dt"/"dx" + 2y` = x2 is ______.
Find the general solution of `"dy"/"dx" + "a"y` = emx
Find the general solution of y2dx + (x2 – xy + y2) dy = 0.
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
If y = e–x (Acosx + Bsinx), then y is a solution of ______.
Solution of differential equation xdy – ydx = 0 represents : ______.
The solution of the differential equation `("d"y)/("d"x) + (2xy)/(1 + x^2) = 1/(1 + x^2)^2` is ______.
The solution of the differential equation ydx + (x + xy)dy = 0 is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
If the solution curve of the differential equation `(dy)/(dx) = (x + y - 2)/(x - y)` passes through the point (2, 1) and (k + 1, 2), k > 0, then ______.
