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:
`cos^2 x dy/dx + y = tan x(0 <= x < pi/2)`
For the differential equation, find the general solution:
`x dy/dx + y - x + xy cot x = 0(x != 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:
`(1 + x^2)dy/dx + 2xy = 1/(1 + x^2); y = 0` when x = 1
Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.
The Integrating Factor of the differential equation `dy/dx - y = 2x^2` is ______.
dx + xdy = e−y sec2 y dy
Solve the differential equation \[\left( x + 2 y^2 \right)\frac{dy}{dx} = y\], given that when x = 2, y = 1.
Find the general solution of the differential equation \[x\frac{dy}{dx} + 2y = x^2\]
Solve the differential equation \[\frac{dy}{dx}\] + y cot x = 2 cos x, given that y = 0 when x = \[\frac{\pi}{2}\] .
Find the integerating factor of the differential equation `x(dy)/(dx) - 2y = 2x^2`
Solve the following differential equation:
`"dy"/"dx" + "y" * sec "x" = tan "x"`
Solve the following differential equation:
`("x + y") "dy"/"dx" = 1`
Solve the following differential equation:
y dx + (x - y2) dy = 0
Solve the following differential equation:
`(1 + "x"^2) "dy"/"dx" + "y" = "e"^(tan^-1 "x")`
If the slope of the tangent to the curve at each of its point is equal to the sum of abscissa and the product of the abscissa and ordinate of the point. Also, the curve passes through the point (0, 1). Find the equation of the curve.
The integrating factor of `(dy)/(dx) + y` = e–x is ______.
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 `x (dy)/(dx) - y = 2x^2` is
If y = y(x) is the solution of the differential equation, `(dy)/(dx) + 2ytanx = sinx, y(π/3)` = 0, then the maximum value of the function y (x) over R is equal to ______.
If the solution curve y = y(x) of the differential equation y2dx + (x2 – xy + y2)dy = 0, which passes through the point (1, 1) and intersects the line y = `sqrt(3) x` at the point `(α, sqrt(3) α)`, then value of `log_e (sqrt(3)α)` is equal to ______.
If sin x is the integrating factor (IF) of the linear differential equation `dy/dx + Py` = Q then P is ______.
Solve:
`xsinx dy/dx + (xcosx + sinx)y` = sin x
