हिंदी

Integrating factor of the differential equation of the form ddPQdxdy+P1x=Q1 is given by ee∫P1dy. - Mathematics

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is True.

Explanation:

I.F. of the given differential equation

`("d"x)/("d"y) + "P"_1x = "Q"` is `"e"^(intP_1dy)`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Differential Equations - Exercise [पृष्ठ २०२]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 9 Differential Equations
Exercise | Q 77.(i) | पृष्ठ २०२

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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


Solve the differential equation ` (1 + x2) dy/dx+y=e^(tan^(−1))x.`


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

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

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

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

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

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

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

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

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

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

\[\frac{dy}{dx}\] = y tan x − 2 sin x


\[\frac{dy}{dx}\] + y tan x = cos x


\[\frac{dy}{dx}\] + y cot x = x2 cot x + 2x


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

The slope of the tangent to the curve at any point is the reciprocal of twice the ordinate at that point. The curve passes through the point (4, 3). Determine its equation.


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


Solve the differential equation: (1 + x2) dy + 2xy dx = cot x dx


Solve the following differential equation :

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


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


`"dy"/"dx" + y` = 5 is a differential equation of the type `"dy"/"dx" + "P"y` = Q but it can be solved using variable separable method also.


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.


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.

The solution of the differential equation `"dy"/"dx" = "k"(50 - "y")` is given by ______.


Solve the differential equation:

`"dy"/"dx" = 2^(-"y")`


The solution of the differential equation `(dx)/(dy) + Px = Q` where P and Q are constants or functions of y, is given by


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) =


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


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 ______.


If y = f(x), f'(0) = f(0) = 1 and if y = f(x) satisfies `(d^2y)/(dx^2) + (dy)/(dx)` = x, then the value of [f(1)] is ______ (where [.] denotes greatest integer function)


Solve the differential equation: 

`dy/dx` = cosec y


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×