मराठी

F(x, y) = x2+y2+yx is a homogeneous function of degree ______.

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प्रश्न

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

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उत्तर

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

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पाठ 9: Differential Equations - Solved Examples [पृष्ठ १८९]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 9 Differential Equations
Solved Examples | Q 22. (iv) | पृष्ठ १८९

संबंधित प्रश्‍न

Solve the differential equation :

`y+x dy/dx=x−y dy/dx`


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.

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


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^2 dy/dx = x^2 - 2y^2 + xy`


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:

`[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


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

`2xy + y^2 - 2x^2  dy/dx = 0; y = 2`   when x  = 1


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


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

(x2 + 3xy + y2) dx − x2 dy = 0


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

(2x2 y + y3) dx + (xy2 − 3x3) 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:
\[\frac{dy}{dx} - \frac{y}{x} + cosec\frac{y}{x} = 0, y\left( 1 \right) = 0\]


Solve the following initial value problem:
\[\left\{ x \sin^2 \left( \frac{y}{x} \right) - y \right\}dx + x dy = 0, y\left( 1 \right) = \frac{\pi}{4}\]


Find the particular solution of the differential equation \[\left( x - y \right)\frac{dy}{dx} = x + 2y\], given that when x = 1, y = 0.


Which of the following is a homogeneous differential equation?


Solve the following differential equation:

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


Solve the following differential equation:

`x * dy/dx - y + x * sin(y/x) = 0`


Solve the following differential equation:

`x^2.  dy/dx = x^2 + xy + y^2`


Solve the following differential equation:

(x2 + 3xy + y2)dx - x2 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) = `(x^2 + y^2)/(x - y)` is a homogeneous function of degree 1.


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


The solution of the equation `dy/dx = (3x − 4y − 2)/(3x − 4y − 3)` is ______.


Which differential equation is called a homogeneous differential equation?


Which dependence is checked on the right-hand side of a homogeneous differential equation?


Which substitutions are chosen for a homogeneous differential equation?


What replacement obtains the final answer after using a homogeneous substitution?


Which sequence correctly states the essential actions for obtaining the final answer of a homogeneous differential equation?


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