Advertisements
Advertisements
प्रश्न
Integrating factor of the differential equation of the form `("d"x)/("d"y) + "P"_1x = "Q"_1` is given by `"e"^(int P_1dy)`.
विकल्प
True
False
उत्तर
This statement is True.
Explanation:
I.F. of the given differential equation
`("d"x)/("d"y) + "P"_1x = "Q"` is `"e"^(intP_1dy)`
APPEARS IN
संबंधित प्रश्न
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 cot x = x2 cot x + 2x
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?
Solve the differential equation: (x + 1) dy – 2xy dx = 0
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"`
`("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 = ______.
Solution of the differential equation of the type `("d"x)/("d"y) + "p"_1x = "Q"_1` is given by x.I.F. = `("I"."F") xx "Q"_1"d"y`.
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.
The solution of the differential equation `"dy"/"dx" = "k"(50 - "y")` is given by ______.
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?
The solution of the differential equation `(dx)/(dy) + Px = Q` where P and Q are constants or functions of y, is given by
If `x (dy)/(dx) = y(log y - log x + 1)`, then the solution of the dx equation is
Find the general solution of the differential equation: (x3 + y3)dy = x2ydx
Let y = y(x) be the solution of the differential equation `xtan(y/x)dy = (ytan(y/x) - x)dx, -1 ≤ x ≤ 1, y(1/2) = π/6`. Then the area of the region bounded by the curves x = 0, x = `1/sqrt(2)` and y = y(x) in the upper half plane is ______.
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 ______.
Solve the differential equation:
`dy/dx` = cosec y