English

F(x, y) = ycos(yx)+xxcos(yx) is not a homogeneous function.

Advertisements
Advertisements

Question

F(x, y) = `(ycos(y/x) + x)/(xcos(y/x))` is not a homogeneous function.

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is True.

Explanation:

Because f(λx, λy) = λ°f(x, y).

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Solved Examples [Page 191]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 9 Differential Equations
Solved Examples | Q 23. (iv) | Page 191

RELATED QUESTIONS

Solve the differential equation (x2 + y2)dx- 2xydy = 0


Show that the differential equation 2yx/y dx + (y − 2x ex/y) dy = 0 is homogeneous. Find the particular solution of this differential equation, given that x = 0 when y = 1.


 

Show that the differential  equation `2xydy/dx=x^2+3y^2`  is homogeneous and solve it.

 

Find the particular solution of the differential equation:

2y ex/y dx + (y - 2x ex/y) dy = 0 given that x = 0 when y = 1.


Show that the given differential equation is homogeneous and solve them.

(x2 + xy) dy = (x2 + y2) dx


Show that the given differential equation is homogeneous and solve them.

(x – y) dy – (x + y) dx = 0


Show that the given differential equation is homogeneous and solve them.

`x dy/dx - y +  x sin (y/x) = 0`


Show that the given differential equation is homogeneous and solve them.

`(1+e^(x/y))dx + e^(x/y) (1 - x/y)dy = 0`


For the differential equation find a particular solution satisfying the given condition:

(x + y) dy + (x – y) dx = 0; y = 1 when x = 1


For the differential equation find a particular solution satisfying the given condition:

`dy/dx -  y/x + cosec (y/x) = 0; y = 0` when x = 1


A homogeneous differential equation of the from `dx/dy = h (x/y)` can be solved by making the substitution.


Prove that x2 – y2 = c(x2 + y2)2 is the general solution of the differential equation (x3 – 3xy2)dx = (y3 – 3x2y)dy, where C is parameter


\[\left( x^2 + y^2 \right)\frac{dy}{dx} = 8 x^2 - 3xy + 2 y^2\]

(x2 − 2xy) dy + (x2 − 3xy + 2y2) dx = 0


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

\[\left( x - y \right)\frac{dy}{dx} = x + 2y\]

\[y dx + \left\{ x \log\left( \frac{y}{x} \right) \right\} dy - 2x dy = 0\]

Solve the following initial value problem:
 (x2 + y2) dx = 2xy dy, y (1) = 0


Solve the following initial value problem:
\[x e^{y/x} - y + x\frac{dy}{dx} = 0, y\left( e \right) = 0\]


Solve the following initial value problem:
(xy − y2) dx − x2 dy = 0, y(1) = 1


Show that the family of curves for which \[\frac{dy}{dx} = \frac{x^2 + y^2}{2xy}\], is given by \[x^2 - y^2 = Cx\]


Solve the differential equation: x dy - y dx = `sqrt(x^2 + y^2)dx,` given that y = 0 when x = 1.


Solve the following differential equation:

`"y"^2 - "x"^2 "dy"/"dx" = "xy""dy"/"dx"`


Solve the following differential equation:

x dx + 2y dx = 0, when x = 2, y = 1


Solve the following differential equation:

`x^2.  dy/dx = x^2 + xy + y^2`


Solve the following differential equation:

(x2 – y2)dx + 2xy dy = 0


State whether the following statement is True or False:   

A homogeneous differential equation is solved by substituting y = vx and integrating it


F(x, y) = `(sqrt(x^2 + y^2) + y)/x` is a homogeneous function of degree ______.


Solve : `x^2 "dy"/"dx"` = x2 + xy + y2.


Solcve: `x ("d"y)/("d"x) = y(log y – log x + 1)`


A homogeneous differential equation of the `(dx)/(dy) = h(x/y)` can be solved by making the substitution.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×