Advertisements
Advertisements
Question
The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx2.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
The given differential equation is `("d"y)/("d"x) = (x + 2y)/x`
⇒ `("d"y)/("d"x) = 1 + 2 y/x`
⇒ `("d"y)/("d"x) = (2y)/x` = 1
Here, P = `(-2)/x` and Q = 1
Integrating factor I.F. = `"e"^(int(-2)/x "d"x)`
= `"e"^(-2 log x)`
= `"e"^(log x^-2)`
= `1/x^2`
∴ Solution is `y xx "I"."F". = int "Q" xx "I"."F". "d"x + "c"`
⇒ `y xx 1/x^2 = int 1 xx 1/x^2 "d"x + "c"`
⇒ `y/x^2 = int 1/x^2 "d"x + "c"`
⇒ `y/x^2 = - 1/x + "c"`
⇒ y = `-x + "c"x^2`
⇒ y + x = cx2
APPEARS IN
RELATED QUESTIONS
The solution of the differential equation dy/dx = sec x – y tan x is:
(A) y sec x = tan x + c
(B) y sec x + tan x = c
(C) sec x = y tan x + c
(D) sec x + y tan x = c
Solve the differential equation `dy/dx=(y+sqrt(x^2+y^2))/x`
Find the general solution of the following differential equation :
`(1+y^2)+(x-e^(tan^(-1)y))dy/dx= 0`
Find the particular solution of the differential equation `(1+x^2)dy/dx=(e^(mtan^-1 x)-y)` , give that y=1 when x=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 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 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 \[\frac{dy}{dx} = \frac{y}{x}\] is
The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is
The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents
The solution of the differential equation \[\frac{dy}{dx} = \frac{x^2 + xy + y^2}{x^2}\], is
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
\[\frac{dy}{dx} + 1 = e^{x + y}\]
(x + y − 1) dy = (x + y) dx
\[\frac{dy}{dx} - y \tan x = e^x\]
(x2 + 1) dy + (2y − 1) dx = 0
`(2ax+x^2)(dy)/(dx)=a^2+2ax`
\[y - x\frac{dy}{dx} = b\left( 1 + x^2 \frac{dy}{dx} \right)\]
`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`
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:- \[\left( x - y \right)\frac{dy}{dx} = x + 2y\]
Solve the following differential equation:- \[x \cos\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\]
Solve the following differential equation:-
\[\frac{dy}{dx} + 2y = \sin x\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \frac{y}{x} = x^2\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \left( \sec x \right) y = \tan x\]
Find a particular solution of the following differential equation:- x2 dy + (xy + y2) dx = 0; y = 1 when x = 1
Form the differential equation having y = (sin–1x)2 + Acos–1x + B, where A and B are arbitrary constants, as its general solution.
Solve: `y + "d"/("d"x) (xy) = x(sinx + logx)`
Find the general solution of `("d"y)/("d"x) -3y = sin2x`
The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is ______.
Solution of differential equation xdy – ydx = 0 represents : ______.
The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is ______.
The solution of differential equation coty dx = xdy is ______.
The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` is ______.
