मराठी

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

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प्रश्न

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

पर्याय

  • x2 + 2xy

  • 2x – y

  • `cos^2 (y/x) + y/x`

  • sinx – cosy

MCQ

उत्तर

sinx – cosy

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पाठ 9: Differential Equations - Solved Examples [पृष्ठ १८८]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 9 Differential Equations
Solved Examples | Q 19 | पृष्ठ १८८

संबंधित प्रश्‍न

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.

`y  dx + x log(y/x)dy - 2x  dy = 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`


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


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

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


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

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

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

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

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:
(xy − y2) dx − x2 dy = 0, y(1) = 1


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


Which of the following is a homogeneous differential equation?


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Solve the following differential equation:

y2 dx + (xy + x2)dy = 0


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


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


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


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 ______.


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