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 = ______.
Advertisements
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`
Solve the differential equation ` (1 + x2) dy/dx+y=e^(tan^(−1))x.`
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
Find the equation of the 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.
Experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment. Its half-life is 1590 years. What percentage will disappear in one year?
A wet porous substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost 95% moisture, weather conditions remaining the same.
Solve the differential equation: (x + 1) dy – 2xy dx = 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.
`("d"y)/("d"x) + y/(xlogx) = 1/x` is an equation of the type ______.
Integrating factor of the differential equation of the form `("d"x)/("d"y) + "P"_1x = "Q"_1` is given by `"e"^(int P_1dy)`.
Correct substitution for the solution of the differential equation of the type `("d"x)/("d"y) = "g"(x, y)` where g(x, y) is a homogeneous function of the degree zero is x = vy.
Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.
Which of the following solutions may be used to find the number of children who have been given the polio drops?
If `x (dy)/(dx) = y(log y - log x + 1)`, then the solution of the dx equation is
Solve the differential equation: xdy – ydx = `sqrt(x^2 + y^2)dx`
Solve the following differential equation: (y – sin2x)dx + tanx dy = 0
Find the general solution of the differential equation: (x3 + y3)dy = x2ydx
Let y = y(x) be the solution of the differential equation `(dy)/(dx) + (sqrt(2)y)/(2cos^4x - cos2x) = xe^(tan^-1(sqrt(2)cost2x)), 0 < x < π/2` with `y(π/4) = π^2/32`. If `y(π/3) = π^2/18e^(-tan^-1(α))`, then the value of 3α2 is equal to ______.
If y = y(x) is the solution of the differential equation `(1 + e^(2x))(dy)/(dx) + 2(1 + y^2)e^x` = 0 and y(0) = 0, then `6(y^'(0) + (y(log_esqrt(3))))^2` is equal to ______.
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 `e^xsqrt(1 - y^2)dx + (y/x)dy` = 0, y(1) = –1. Then, the value of (y(3))2 is equal to ______.
Let y = y(x) be the solution of the differential equation, `(2 + sinxdy)/(y + 1) (dy)/(dx)` = –cosx. If y > 0, y(0) = 1. If y(π) = a, and `(dy)/(dx)` at x = π is b, then the ordered pair (a, b) is equal to ______.
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)
