Advertisements
Advertisements
Question
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.
Options
x
logx
`1/x`
– x
Advertisements
Solution
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is `1/x`.
Explanation:
The given differential equation is `x ("d"y)/("d"x) - y = x^4 - 3x`
⇒ `("d"y)/("d"x) - y/x = x^3 - 3`
Here, P = `- 1/x` and Q = `x^3 - 3`
So, integrating factor = `"e"^(int Pdx)`
= `"e"^(int 1/x "d"x)`
= `"e"^(-logx)`
= `"e"^(log 1/x)`
= `1/x`.
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
The differential equation of the family of curves y=c1ex+c2e-x is......
(a)`(d^2y)/dx^2+y=0`
(b)`(d^2y)/dx^2-y=0`
(c)`(d^2y)/dx^2+1=0`
(d)`(d^2y)/dx^2-1=0`
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
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 particular solution of a differential equation of third order are ______.
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 x dx + y dy = x2 y dy − y2 x dx, is
The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is
Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .
\[\frac{dy}{dx} + \frac{y}{x} = \frac{y^2}{x^2}\]
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
\[\frac{dy}{dx} - y \tan x = - 2 \sin x\]
\[\frac{dy}{dx} - y \tan x = e^x\]
(x2 + 1) dy + (2y − 1) dx = 0
\[x\frac{dy}{dx} + x \cos^2 \left( \frac{y}{x} \right) = y\]
\[\left( 1 + y^2 \right) + \left( x - e^{- \tan^{- 1} y} \right)\frac{dy}{dx} = 0\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \left( 1 + x^2 \right)\left( 1 + y^2 \right)\]
For the following differential equation, find a particular solution satisfying the given condition:- \[\cos\left( \frac{dy}{dx} \right) = a, y = 1\text{ when }x = 0\]
For the following differential equation, find a particular solution satisfying the given condition:- \[\frac{dy}{dx} = y \tan x, y = 1\text{ when }x = 0\]
Solve the following differential equation:-
\[x\frac{dy}{dx} + 2y = x^2 , x \neq 0\]
Solve the following differential equation:-
\[\frac{dy}{dx} + 2y = \sin x\]
Solve the following differential equation:-
\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]
Find a particular solution of the following differential equation:- \[\left( 1 + x^2 \right)\frac{dy}{dx} + 2xy = \frac{1}{1 + x^2}; y = 0,\text{ when }x = 1\]
Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x2 + 1) dx, x ≠ 0.
The solution of the differential equation `x "dt"/"dx" + 2y` = x2 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 the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.
Solve: `y + "d"/("d"x) (xy) = x(sinx + logx)`
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.
Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.
General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.
The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.
General solution of `("d"y)/("d"x) + y` = sinx is ______.
The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
Find the general solution of the differential equation:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
