Advertisements
Advertisements
प्रश्न
`("e"^(-2sqrt(x))/sqrt(x) - y/sqrt(x))("d"x)/("d"y) = 1(x ≠ 0)` when written in the form `"dy"/"dx" + "P"y` = Q, then P = ______.
उत्तर
`("e"^(-2sqrt(x))/sqrt(x) - y/sqrt(x))("d"x)/("d"y) = 1(x ≠ 0)` when written in the form `"dy"/"dx" + "P"y` = Q, then P = `1/sqrt(x)`.
Explanation:
`1/sqrt(x)`; the given equation can be written as
`"dy"/"dx" = ("e"^(-2sqrt(x)))/sqrt(x) - y/sqrt(x)`
i.e. `"dy"/"dx" + y/sqrt(x) = ("e"^(-2sqrt(x)))/sqrt(x)`
This is a differential equation of the type `"dy"/"dx" + "P"y` = Q.
APPEARS IN
संबंधित प्रश्न
Find the integrating factor for the following differential equation:`x logx dy/dx+y=2log x`
Find the integrating factor of the differential equation.
`((e^(-2^sqrtx))/sqrtx-y/sqrtx)dy/dx=1`
Solve `sin x dy/dx - y = sin x.tan x/2`
\[\frac{dy}{dx}\] = y tan x − 2 sin x
\[\frac{dy}{dx}\] + y tan x = cos x
The slope of the tangent to the curve at any point is the reciprocal of twice the ordinate at that point. The curve passes through the point (4, 3). Determine its equation.
Solve the differential equation: (x + 1) dy – 2xy dx = 0
Solve the differential equation: (1 + x2) dy + 2xy dx = cot x dx
Solve the differential equation : `"x"(d"y")/(d"x") + "y" - "x" + "xy"cot"x" = 0; "x" != 0.`
Solve the following differential equation :
`"dy"/"dx" + "y" = cos"x" - sin"x"`
`"dy"/"dx" + y` = 5 is a differential equation of the type `"dy"/"dx" + "P"y` = Q but it can be solved using variable separable method also.
If ex + ey = ex+y, then `"dy"/"dx"` is:
Solve the differential equation:
`"dy"/"dx" = 2^(-"y")`
The solution of the differential equation `(dx)/(dy) + Px = Q` where P and Q are constants or functions of y, is given by
The solution of the differential equation `(dy)/(dx) = 1 + x + y + xy` when y = 0 at x = – 1 is
If `x (dy)/(dx) = y(log y - log x + 1)`, then the solution of the dx equation is
Solve the following differential equation: (y – sin2x)dx + tanx dy = 0
The population P = P(t) at time 't' of a certain species follows the differential equation `("dp")/("dt")` = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is ______.
Let y = y(x) be the solution of the differential equation, `(x^2 + 1)^2 ("dy")/("d"x) + 2x(x^2 + 1)"y"` = 1, such that y(0) = 0. If `sqrt("ay")(1) = π/32` then the value of 'a' is ______.
If y = f(x), f'(0) = f(0) = 1 and if y = f(x) satisfies `(d^2y)/(dx^2) + (dy)/(dx)` = x, then the value of [f(1)] is ______ (where [.] denotes greatest integer function)
The solution of the differential equation `(1 + y^2) + (x - e^(tan^-1y)) (dy)/(dx)` = 0, is ______.
