Advertisements
Advertisements
Question
Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.
Options
x(y + cosx) = sinx + c
x(y – cosx) = sinx + c
xy cosx = sinx + c
x(y + cosx) = cosx + c
Advertisements
Solution
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
RELATED QUESTIONS
The differential equation of `y=c/x+c^2` is :
(a)`x^4(dy/dx)^2-xdy/dx=y`
(b)`(d^2y)/dx^2+xdy/dx+y=0`
(c)`x^3(dy/dx)^2+xdy/dx=y`
(d)`(d^2y)/dx^2+dy/dx-y=0`
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
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:
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:
x + y = tan–1y : y2 y′ + y2 + 1 = 0
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
`y = sqrt(a^2 - x^2 ) x in (-a,a) : x + y dy/dx = 0(y != 0)`
The number of arbitrary constants in the general solution of a differential equation of fourth order are ______.
If y = etan x+ (log x)tan x then find dy/dx
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.
How many arbitrary constants are there in the general solution of the differential equation of order 3.
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
The solution of x2 + y2 \[\frac{dy}{dx}\]= 4, is
The solution of the differential equation \[\frac{dy}{dx} = \frac{x^2 + xy + y^2}{x^2}\], is
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is
Find the particular solution of the differential equation `(1+y^2)+(x-e^(tan-1 )y)dy/dx=` given that y = 0 when x = 1.
Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .
\[\frac{dy}{dx} + 1 = e^{x + y}\]
\[\frac{dy}{dx} = \left( x + y \right)^2\]
For the following differential equation, find a particular solution satisfying the given condition:
\[x\left( x^2 - 1 \right)\frac{dy}{dx} = 1, y = 0\text{ when }x = 2\]
For the following differential equation, find a particular solution satisfying the given condition:- \[\cos\left( \frac{dy}{dx} \right) = a, y = 1\text{ when }x = 0\]
Solve the following differential equation:-
\[x\frac{dy}{dx} + 2y = x^2 , x \neq 0\]
Solve the following differential equation:-
(1 + x2) dy + 2xy dx = cot x dx
Solve the differential equation: `(d"y")/(d"x") - (2"x")/(1+"x"^2) "y" = "x"^2 + 2`
Solve the differential equation: ` ("x" + 1) (d"y")/(d"x") = 2e^-"y" - 1; y(0) = 0.`
Solution of the differential equation `"dx"/x + "dy"/y` = 0 is ______.
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
x + y = tan–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.
Find the general solution of `"dy"/"dx" + "a"y` = emx
Form the differential equation having y = (sin–1x)2 + Acos–1x + B, where A and B are arbitrary constants, as its general solution.
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.
Find the particular solution of the following differential equation, given that y = 0 when x = `pi/4`.
`(dy)/(dx) + ycotx = 2/(1 + sinx)`
Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0
Solve the differential equation:
`(xdy - ydx) ysin(y/x) = (ydx + xdy) xcos(y/x)`.
Find the particular solution satisfying the condition that y = π when x = 1.
