Advertisements
Advertisements
प्रश्न
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.
विकल्प
True
False
उत्तर
This statement is True.
Explanation:
Since particular solution of a differential equation has no arbitrary constant.
APPEARS IN
संबंधित प्रश्न
Solve the following differential equation: `(x^2-1)dy/dx+2xy=2/(x^2-1)`
Find the integrating factor for the following differential equation:`x logx dy/dx+y=2log x`
Solve `sin x dy/dx - y = sin x.tan x/2`
Solve the differential equation `sin^(-1) (dy/dx) = x + y`
\[\frac{dy}{dx}\] + y tan x = cos x
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: (1 + x2) dy + 2xy dx = cot x dx
Solve the differential equation `"dy"/"dx" + y/x` = x2.
`("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 = ______.
Integrating factor of the differential equation of the form `("d"x)/("d"y) + "P"_1x = "Q"_1` is given by `"e"^(int P_1dy)`.
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`.
If ex + ey = ex+y, then `"dy"/"dx"` is:
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 α, β are different values of x satisfying the equation a cos x + b sinα x = c, where a, b and c are constants, then `tan ((alpha + beta)/2)` is
`int cos(log x) dx = F(x) + C` where C is arbitrary constant. Here F(x) =
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 ______.
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 ______.
Solve the differential equation:
`dy/dx` = cosec y
