मराठी

Correct substitution for the solution of the differential equation of the type ddfdydx=f(x,y), where f(x, y) is a homogeneous function of zero degree is y = vx. - Mathematics

Advertisements
Advertisements

प्रश्न

Correct substitution for the solution of the differential equation of the type `("d"y)/("d"x) = "f"(x, y)`, where f(x, y) is a homogeneous function of zero degree is y = vx.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
Advertisements

उत्तर

This statement is True.

Explanation:

Since particular solution of a differential equation has no arbitrary constant.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Equations - Exercise [पृष्ठ २०३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 9 Differential Equations
Exercise | Q 77.(iii) | पृष्ठ २०३

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Solve the following differential equation: `(x^2-1)dy/dx+2xy=2/(x^2-1)`


Find the integrating factor for the following differential equation:`x logx dy/dx+y=2log x`


\[\frac{dy}{dx} + 2y = e^{3x}\]

\[\frac{dy}{dx} + 2y = 6 e^x\]

\[\frac{dy}{dx} + 2y = 4x\]

\[x\frac{dy}{dx} - y = \left( x - 1 \right) e^x\]

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

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

\[\frac{dy}{dx}\] = y tan x − 2 sin x


\[\left( 1 + x^2 \right)\frac{dy}{dx} + y = \tan^{- 1} x\]

\[\frac{dy}{dx}\] + y tan x = cos x


\[\left( 1 + y^2 \right) + \left( x - e^{tan^{- 1} y} \right)\frac{dy}{dx} = 0\]

The decay rate of radium at any time  t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.


Experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment. Its half-life is 1590 years. What percentage will disappear in one year?


A wet porous substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost 95% moisture, weather conditions remaining the same.


Solve the differential equation: (x + 1) dy – 2xy dx = 0


Solve the differential equation : `"x"(d"y")/(d"x") + "y" - "x" + "xy"cot"x" = 0; "x" != 0.`


Solve the following differential equation :

`"dy"/"dx" + "y" = cos"x" - sin"x"`


Solve the differential equation `"dy"/"dx" + y/x` = x2.


`("e"^(-2sqrt(x))/sqrt(x) - y/sqrt(x))("d"x)/("d"y) = 1(x ≠ 0)` when written in the form `"dy"/"dx" + "P"y` = Q, then P = ______.


`("d"y)/("d"x) + y/(xlogx) = 1/x` is an equation of the type ______.


Integrating factor of the differential equation of the form `("d"x)/("d"y) + "P"_1x = "Q"_1` is given by `"e"^(int P_1dy)`.


Solution of the differential equation of the type `("d"x)/("d"y) + "p"_1x = "Q"_1` is given by x.I.F. = `("I"."F") xx "Q"_1"d"y`.


Correct substitution for the solution of the differential equation of the type `("d"x)/("d"y) = "g"(x, y)` where g(x, y) is a homogeneous function of the degree zero is x = vy.


Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

Which of the following solutions may be used to find the number of children who have been given the polio drops?


The solution of the differential equation `(dy)/(dx) = 1 + x + y + xy` when y = 0 at x = – 1 is


`int cos(log x)  dx = F(x) + C` where C is arbitrary constant. Here F(x) =


Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.


Solve the differential equation: xdy – ydx = `sqrt(x^2 + y^2)dx`


Let y = y(x) be the solution of the differential equation `(dy)/(dx) + (sqrt(2)y)/(2cos^4x - cos2x) = xe^(tan^-1(sqrt(2)cost2x)), 0 < x < π/2` with `y(π/4) = π^2/32`. If `y(π/3) = π^2/18e^(-tan^-1(α))`, then the value of 3α2 is equal to ______.


Let y = y(x) be the solution of the differential equation `e^xsqrt(1 - y^2)dx + (y/x)dy` = 0, y(1) = –1. Then, the value of (y(3))2 is equal to ______.


Let y = y(x) be the solution of the differential equation, `(2 + sinxdy)/(y + 1) (dy)/(dx)` = –cosx. If y > 0, y(0) = 1. If y(π) = a, and `(dy)/(dx)` at x = π is b, then the ordered pair (a, b) is equal to ______.


Solve the differential equation: 

`dy/dx` = cosec y


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×