Advertisements
Advertisements
Question
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.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
Since particular solution of a differential equation has no arbitrary constant.
APPEARS IN
RELATED QUESTIONS
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 the differential equation `sin^(-1) (dy/dx) = x + y`
\[\frac{dy}{dx}\] + y tan x = cos x
\[\frac{dy}{dx}\] + y cot x = x2 cot x + 2x
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.
The decay rate of radium at any time t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.
Solve the differential equation: (x + 1) dy – 2xy dx = 0
Solve the following differential equation :
`"dy"/"dx" + "y" = cos"x" - sin"x"`
`("d"y)/("d"x) + y/(xlogx) = 1/x` is an equation of the type ______.
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`.
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 ______.
Solve the differential equation:
`"dy"/"dx" = 2^(-"y")`
`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 ______.
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 ______.
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 ______.
Solve the differential equation:
`dy/dx` = cosec y
