Advertisements
Advertisements
प्रश्न
Integrating factor of the differential equation `x "dy"/"dx" - y` = sinx is ______.
Advertisements
उत्तर
Integrating factor of the differential equation `x "dy"/"dx" - y` = sinx is `1/x`.
Explanation:
`1/x`; given differential equation can be written as `"dy"/"dx" - y/x = sinx/x`
And Therefore I.F. = `"e"^(int 1/x "d"x)`
= `"e"^(-logx)`
= `1/x`.
APPEARS IN
संबंधित प्रश्न
Show that Ax2 + By2 = 1 is a solution of the differential equation x \[\left\{ y\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^2 \right\} = y\frac{dy}{dx}\]
Verify that y = log \[\left( x + \sqrt{x^2 + a^2} \right)^2\] satisfies the differential equation \[\left( a^2 + x^2 \right)\frac{d^2 y}{d x^2} + x\frac{dy}{dx} = 0\]
Differential equation \[x\frac{dy}{dx} = 1, y\left( 1 \right) = 0\]
Function y = log x
Differential equation \[\frac{d^2 y}{d x^2} + y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 1\] Function y = sin x + cos x
(1 − x2) dy + xy dx = xy2 dx
(y2 + 1) dx − (x2 + 1) dy = 0
In a bank principal increases at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 = 1.648).
(x + y) (dx − dy) = dx + dy
\[x^2 \frac{dy}{dx} = x^2 + xy + y^2 \]
(y2 − 2xy) dx = (x2 − 2xy) dy
2xy dx + (x2 + 2y2) dy = 0
Solve the following initial value problem:-
\[\frac{dy}{dx} + y\cot x = 2\cos x, y\left( \frac{\pi}{2} \right) = 0\]
A population grows at the rate of 5% per year. How long does it take for the population to double?
In a culture, the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present?
The decay rate of radium at any time t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.
The slope of the tangent at a point P (x, y) on a curve is \[\frac{- x}{y}\]. If the curve passes through the point (3, −4), find the equation of the curve.
The tangent at any point (x, y) of a curve makes an angle tan−1(2x + 3y) with x-axis. Find the equation of the curve if it passes through (1, 2).
The solution of the differential equation \[\frac{dy}{dx} - \frac{y\left( x + 1 \right)}{x} = 0\] is given by
Which of the following transformations reduce the differential equation \[\frac{dz}{dx} + \frac{z}{x}\log z = \frac{z}{x^2} \left( \log z \right)^2\] into the form \[\frac{du}{dx} + P\left( x \right) u = Q\left( x \right)\]
What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?
Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y \sin x = 1\], is
Form the differential equation of the family of circles having centre on y-axis and radius 3 unit.
Solve the following differential equation.
`y^3 - dy/dx = x dy/dx`
Solve the following differential equation.
y2 dx + (xy + x2 ) dy = 0
Solve the following differential equation.
x2y dx − (x3 + y3) dy = 0
Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0
Choose the correct alternative:
Differential equation of the function c + 4yx = 0 is
