English

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

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

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

RELATED QUESTIONS

 

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.

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


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`


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


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

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

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

(x2 + 3xy + y2) dx − x2 dy = 0


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

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

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


Solve the following initial value problem:
(y4 − 2x3 y) dx + (x4 − 2xy3) 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 \[x^2 - y^2 = Cx\]


A homogeneous differential equation of the form \[\frac{dx}{dy} = h\left( \frac{x}{y} \right)\] can be solved by making the substitution


Solve the differential equation:  ` (dy)/(dx) = (x + y )/ (x - y )`


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:

(9x + 5y) dy + (15x + 11y)dx = 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) = `(ycos(y/x) + x)/(xcos(y/x))` is not a homogeneous function.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×