मराठी

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

Advertisements
Advertisements

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
Advertisements

उत्तर

sinx – cosy

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Equations - Solved Examples [पृष्ठ १८८]

APPEARS IN

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

संबंधित प्रश्‍न

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.

 

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 – y) dy – (x + y) dx = 0


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

(x + y) dy + (x – y) dx = 0; y = 1 when x = 1


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:

`[xsin^2(y/x - y)] dx + x  dy = 0; y = pi/4 "when"  x = 1`


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


Which of the following is a homogeneous differential equation?


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.


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

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


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

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

(2x2 y + y3) dx + (xy2 − 3x3) dy = 0


Solve the following initial value problem:
(y4 − 2x3 y) dx + (x4 − 2xy3) 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, \[y = \frac{\pi}{4}\]


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


Which of the following is a homogeneous differential equation?


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:

y2 dx + (xy + x2)dy = 0


Solve the following differential equation:

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


Solve the following differential equation:

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


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


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


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


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


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 ______.


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


From \[v+x\frac{dv}{dx}=\frac{v\cos v+1}{\cos v}\], what is \[x\frac{dv}{dx}\]?


Which final answer results after replacing \[v=\frac{y}{x}\] in \[\sin v=\ln|Cx|\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×