English

Which of the following is not a homogeneous function of x and y.

Advertisements
Advertisements

Question

Which of the following is not a homogeneous function of x and y.

Options

  • x2 + 2xy

  • 2x – y

  • `cos^2 (y/x) + y/x`

  • sinx – cosy

MCQ
Advertisements

Solution

sinx – cosy

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Solved Examples [Page 188]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 9 Differential Equations
Solved Examples | Q 19 | Page 188

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.

 

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.

(x2 – y2) dx + 2xy dy = 0


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

`x^2 dy/dx = x^2 - 2y^2 + xy`


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

`x  dy - y  dx =  sqrt(x^2 + y^2)   dx`


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.

`y  dx + x log(y/x)dy - 2x  dy = 0`


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

`[xsin^2(y/x - y)] dx + x  dy = 0; y = pi/4 "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 differential equation  (x3 – 3x y2) dx = (y3 – 3x2y) dy, where c is a parameter.


Find the particular solution of the differential equation `(x - y) dy/dx = (x + 2y)` given that y = 0 when x = 1.


(x2 − 2xy) dy + (x2 − 3xy + 2y2) dx = 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:
\[\frac{dy}{dx} - \frac{y}{x} + cosec\frac{y}{x} = 0, y\left( 1 \right) = 0\]


Solve the following initial value problem:
(y4 − 2x3 y) dx + (x4 − 2xy3) dy = 0, y (1) = 1


Solve the following initial value problem:
x (x2 + 3y2) dx + y (y2 + 3x2) dy = 0, y (1) = 1


Find the particular solution of the differential equation x cos\[\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\], given that when x = 1, \[y = \frac{\pi}{4}\]


Solve the following differential equation : \[\left[ y - x  \cos\left( \frac{y}{x} \right) \right]dy + \left[ y  \cos\left( \frac{y}{x} \right) - 2x  \sin\left( \frac{y}{x} \right) \right]dx = 0\] .


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:

`(1 + 2"e"^("x"/"y")) + 2"e"^("x"/"y")(1 - "x"/"y") "dy"/"dx" = 0`


Solve the following differential equation:

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


Solve the following differential equation:

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


Solve the following differential equation:

`"xy" "dy"/"dx" = "x"^2 + "2y"^2, "y"(1) = 0`


Solve the following differential equation:

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


Solve the following differential equation:

(x2 + 3xy + y2)dx - x2 dy = 0


Solve the following differential equation:

(x2 – y2)dx + 2xy dy = 0


Find the equation of a curve passing through `(1, pi/4)` if the slope of the tangent to the curve at any point P(x, y) is `y/x - cos^2  y/x`.


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


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.


Let the solution curve of the differential equation `x (dy)/(dx) - y = sqrt(y^2 + 16x^2)`, y(1) = 3 be y = y(x). Then y(2) is equal to ______.


The solution of the differential equation y2 dx + (x2 − xy + y2)dy = 0 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×