मराठी

The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.

रिकाम्या जागा भरा
Advertisements

उत्तर

The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is Zero; any particular solution of a differential equation has no arbitrary constant.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Equations - Solved Examples [पृष्ठ १८९]

APPEARS IN

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

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

If x = Φ(t) differentiable function of ‘ t ' then prove that `int f(x) dx=intf[phi(t)]phi'(t)dt`


Solve the differential equation `dy/dx=(y+sqrt(x^2+y^2))/x`


Find the particular solution of the differential equation  `e^xsqrt(1-y^2)dx+y/xdy=0` , given that y=1 when x=0


Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

y = Ax : xy′ = y (x ≠ 0)


Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

y = x sin x : xy' = `y + x  sqrt (x^2 - y^2)`  (x ≠ 0 and x > y or x < -y)


Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

xy = log y + C :  `y' = (y^2)/(1 - xy) (xy != 1)`


The number of arbitrary constants in the particular solution of a differential equation of third order are ______.


Find a particular solution of the differential equation `dy/dx + y cot x = 4xcosec x(x != 0)`, given that y = 0 when `x = pi/2.`


if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`


Write the order of the differential equation associated with the primitive y = C1 + C2 ex + C3 e−2x + C4, where C1, C2, C3, C4 are arbitrary constants.


How many arbitrary constants are there in the general solution of the differential equation of order 3.


The general solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x}\] is


The general solution of the differential equation \[\frac{dy}{dx} + y\] g' (x) = g (x) g' (x), where g (x) is a given function of x, is


The solution of the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + 1 + y^2 = 0\], is


Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .


Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\] given that

\[y = \frac{\pi}{2}\] when x = 1.

The solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x} + \frac{\phi\left( \frac{y}{x} \right)}{\phi'\left( \frac{y}{x} \right)}\] is


\[\frac{dy}{dx} = \frac{\sin x + x \cos x}{y\left( 2 \log y + 1 \right)}\]


\[\frac{dy}{dx} + 1 = e^{x + y}\]


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


(x3 − 2y3) dx + 3x2 y dy = 0


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


\[\cos^2 x\frac{dy}{dx} + y = \tan x\]


`x cos x(dy)/(dx)+y(x sin x + cos x)=1`


`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`


For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sqrt{4 - y^2}, - 2 < y < 2\]


Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x-coordinate and the product of the x-coordinate and y-coordinate of that point.


The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.


Find the general solution of `(x + 2y^3)  "dy"/"dx"` = y


Solve:

`2(y + 3) - xy  (dy)/(dx)` = 0, given that y(1) = – 2.


Find the general solution of `("d"y)/("d"x) -3y = sin2x`


Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.


Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.


y = aemx+ be–mx satisfies which of the following differential equation?


The differential equation for which y = acosx + bsinx is a solution, is ______.


General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.


The solution of `("d"y)/("d"x) = (y/x)^(1/3)` is `y^(2/3) - x^(2/3)` = c.


Find the particular solution of the following differential equation, given that y = 0 when x = `pi/4`.

`(dy)/(dx) + ycotx = 2/(1 + sinx)`


Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×