हिंदी

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

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is True.

Explanation:

Because f(λx, λy) = λ°f(x, y).

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Differential Equations - Solved Examples [पृष्ठ १९१]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 9 Differential Equations
Solved Examples | Q 23. (iv) | पृष्ठ १९१

संबंधित प्रश्न

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


Solve the differential equation :

`y+x dy/dx=x−y dy/dx`


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.

`y' = (x + y)/x`


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.

`{xcos(y/x) + ysin(y/x)}ydx = {ysin (y/x) -  xcos(y/x)}xdy`


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:

x2 dy + (xy + y2) 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


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


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

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


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

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

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

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:
\[\frac{dy}{dx} = \frac{y\left( x + 2y \right)}{x\left( 2x + y \right)}, y\left( 1 \right) = 2\]

 


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


Which of the following is a homogeneous differential equation?


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 following differential equation:

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


Solve the following differential equation:

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


Solve the following differential equation:

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


Solve the following differential equation:

(9x + 5y) dy + (15x + 11y)dx = 0


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


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


F(x, y) = `(x^2 + y^2)/(x - y)` is a homogeneous function of degree 1.


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


The solution of the differential equation `(1 + e^(x/y)) dx + e^(x/y) (1 + x/y) dy` = 0 is


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


If a curve y = f(x), passing through the point (1, 2), is the solution of the differential equation, 2x2dy = (2xy + y2)dx, then `f(1/2)` is equal to ______.


Find the general solution of the differential equation:

(xy – x2) dy = y2 dx


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×