Advertisements
Advertisements
प्रश्न
Find the integerating factor of the differential equation `xdy/dx - 2y = 2x^2` .
उत्तर
`dy/dx + (-2/x)y = 2x`
compare with `dy/dx + py = Q`
⇒ `p = -2/x`
`therefore` Integrating factor `IF = e^(∫pdx)`
= `e^(∫-2/xdx)`
= `e^(-2"In "x)`
= `e^("In" x^-2)`
= `x^-2`
= `1/x^2`
APPEARS IN
संबंधित प्रश्न
Find the the differential equation for all the straight lines, which are at a unit distance from the origin.
For the differential equation, find the general solution:
`dy/dx + y/x = x^2`
For the differential equation, find the general solution:
`dy/dx + (sec x) y = tan x (0 <= x < pi/2)`
For the differential equation, find the general solution:
`x log x dy/dx + y= 2/x log x`
For the differential equation, find the general solution:
(1 + x2) dy + 2xy dx = cot x dx (x ≠ 0)
For the differential equation, find the general solution:
y dx + (x – y2) dy = 0
For the differential equation given, find a particular solution satisfying the given condition:
`dy/dx + 2y tan x = sin x; y = 0 " when x " = pi/3`
For the differential equation given, find a particular solution satisfying the given condition:
`dy/dx - 3ycotx = sin 2x; y = 2` when `x = pi/2`
The integrating factor of the differential equation.
`(1 - y^2) dx/dy + yx = ay(-1 < y < 1)` is ______.
dx + xdy = e−y sec2 y dy
Solve the following differential equation: \[\left( \cot^{- 1} y + x \right) dy = \left( 1 + y^2 \right) dx\] .
Solve the differential equation: `(1 + x^2) dy/dx + 2xy - 4x^2 = 0,` subject to the initial condition y(0) = 0.
Solve the following differential equation dr + (2r cot θ + sin 2θ) dθ = 0.
Solve the following differential equation:
`(1 + "x"^2) "dy"/"dx" + "y" = "e"^(tan^-1 "x")`
The curve passes through the point (0, 2). The sum of the coordinates of any point on the curve exceeds the slope of the tangent to the curve at any point by 5. Find the equation of the curve.
Form the differential equation of all circles which pass through the origin and whose centers lie on X-axis.
The integrating factor of the differential equation sin y `("dy"/"dx")` = cos y(1 - x cos y) is ______.
The integrating factor of the differential equation (1 + x2)dt = (tan-1 x - t)dx is ______.
The equation x2 + yx2 + x + y = 0 represents
State whether the following statement is true or false.
The integrating factor of the differential equation `(dy)/(dx) + y/x` = x3 is – x.
Let y = y(x), x > 1, be the solution of the differential equation `(x - 1)(dy)/(dx) + 2xy = 1/(x - 1)`, with y(2) = `(1 + e^4)/(2e^4)`. If y(3) = `(e^α + 1)/(βe^α)`, then the value of α + β is equal to ______.
The slope of the tangent to the curve x = sin θ and y = cos 2θ at θ = `π/6` is ______.
