हिंदी

Integrating factor of the differential equation dydxdydx-y = cos x is ex. - Mathematics

Advertisements
Advertisements

प्रश्न

Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is ex.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

This statement is False.

Explanation:

Because I.F = `"e"^(int -1 "d"x)`

= e–x.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Differential Equations - Solved Examples [पृष्ठ १९१]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 9 Differential Equations
Solved Examples | Q 23. (vi) | पृष्ठ १९१

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

\[\sqrt[3]{\frac{d^2 y}{d x^2}} = \sqrt{\frac{dy}{dx}}\]

Form the differential equation representing the family of ellipses having centre at the origin and foci on x-axis.


Verify that y = \[\frac{a}{x} + b\] is a solution of the differential equation
\[\frac{d^2 y}{d x^2} + \frac{2}{x}\left( \frac{dy}{dx} \right) = 0\]


Differential equation \[\frac{d^2 y}{d x^2} + y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 1\] Function y = sin x + cos x


Differential equation \[\frac{d^2 y}{d x^2} - 2\frac{dy}{dx} + y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 2\] Function y = xex + ex


\[\frac{dy}{dx} = x^2 + x - \frac{1}{x}, x \neq 0\]

\[\left( x^3 + x^2 + x + 1 \right)\frac{dy}{dx} = 2 x^2 + x\]

Solve the following differential equation:
\[\left( 1 + y^2 \right) \tan^{- 1} xdx + 2y\left( 1 + x^2 \right)dy = 0\]


Find the particular solution of edy/dx = x + 1, given that y = 3, when x = 0.


Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\]  given that y = 1, when x = 0.


In a culture the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present.


(x2 − y2) dx − 2xy dy = 0


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

Solve the following initial value problem:
\[x\frac{dy}{dx} + y = x \cos x + \sin x, y\left( \frac{\pi}{2} \right) = 1\]


If the marginal cost of manufacturing a certain item is given by C' (x) = \[\frac{dC}{dx}\] = 2 + 0.15 x. Find the total cost function C (x), given that C (0) = 100.

 

Show that all curves for which the slope at any point (x, y) on it is \[\frac{x^2 + y^2}{2xy}\]  are rectangular hyperbola.


Write the differential equation obtained by eliminating the arbitrary constant C in the equation x2 − y2 = C2.


The integrating factor of the differential equation (x log x)
\[\frac{dy}{dx} + y = 2 \log x\], is given by


The solution of the differential equation y1 y3 = y22 is


In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

y = ex + 1            y'' − y' = 0


If a + ib = `("x" + "iy")/("x" - "iy"),` prove that `"a"^2 +"b"^2 = 1` and `"b"/"a" = (2"xy")/("x"^2 - "y"^2)`


Solve the following differential equation.

y dx + (x - y2 ) dy = 0


Solve the following differential equation.

`(x + a) dy/dx = – y + a`


Select and write the correct alternative from the given option for the question

Bacterial increases at the rate proportional to the number present. If original number M doubles in 3 hours, then number of bacteria will be 4M in


Select and write the correct alternative from the given option for the question 

Differential equation of the function c + 4yx = 0 is


Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0


Choose the correct alternative:

Solution of the equation `x("d"y)/("d"x)` = y log y is


Verify y = `a + b/x` is solution of `x(d^2y)/(dx^2) + 2 (dy)/(dx)` = 0

y = `a + b/x`

`(dy)/(dx) = square`

`(d^2y)/(dx^2) = square`

Consider `x(d^2y)/(dx^2) + 2(dy)/(dx)`

= `x square + 2 square`

= `square`

Hence y = `a + b/x` is solution of `square`


There are n students in a school. If r % among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?


Solve the differential equation

`y (dy)/(dx) + x` = 0


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×