English

Correct substitution for the solution of the differential equation of the type ddfdydx=f(x,y), where f(x, y) is a homogeneous function of zero degree is y = vx. - Mathematics

Advertisements
Advertisements

Question

Correct substitution for the solution of the differential equation of the type `("d"y)/("d"x) = "f"(x, y)`, where f(x, y) is a homogeneous function of zero degree is y = vx.

Options

  • True

  • False

MCQ
True or False

Solution

This statement is True.

Explanation:

Since particular solution of a differential equation has no arbitrary constant.

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Exercise [Page 203]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 9 Differential Equations
Exercise | Q 77.(iii) | Page 203

RELATED QUESTIONS

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`


\[\frac{dy}{dx} + y = e^{- 2x}\]

\[x\frac{dy}{dx} + y = x e^x\]

\[x\frac{dy}{dx} - y = \left( x - 1 \right) e^x\]

\[\frac{dy}{dx} + \frac{y}{x} = x^3\]

\[\frac{dy}{dx} + 2y = \sin x\]

\[\frac{dy}{dx}\] = y tan x − 2 sin x


\[\left( 1 + y^2 \right) + \left( x - e^{tan^{- 1} y} \right)\frac{dy}{dx} = 0\]

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"`


`("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 = ______.


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?


Solve the differential equation:

`"dy"/"dx" = 2^(-"y")`


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


If `x (dy)/(dx) = y(log y - log x + 1)`, then the solution of the dx equation is


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×