मराठी

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.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

This statement is False.

Explanation:

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

= e–x.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Equations - Solved Examples [पृष्ठ १९१]

APPEARS IN

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

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Prove that:

`int_0^(2a)f(x)dx = int_0^af(x)dx + int_0^af(2a - x)dx`


\[\sqrt{1 + \left( \frac{dy}{dx} \right)^2} = \left( c\frac{d^2 y}{d x^2} \right)^{1/3}\]

Show that Ax2 + By2 = 1 is a solution of the differential equation x \[\left\{ y\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^2 \right\} = y\frac{dy}{dx}\]

 


Verify that y2 = 4a (x + a) is a solution of the differential equations
\[y\left\{ 1 - \left( \frac{dy}{dx} \right)^2 \right\} = 2x\frac{dy}{dx}\]


\[\cos x\frac{dy}{dx} - \cos 2x = \cos 3x\]

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

(1 + x2) dy = xy dx


x cos2 y  dx = y cos2 x dy


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

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

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

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

\[\frac{dy}{dx} = \frac{\left( x - y \right) + 3}{2\left( x - y \right) + 5}\]

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

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

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

3x2 dy = (3xy + y2) dx


\[\left[ x\sqrt{x^2 + y^2} - y^2 \right] dx + xy\ dy = 0\]

The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given the number triples in 5 hrs, find how many bacteria will be present after 10 hours. Also find the time necessary for the number of bacteria to be 10 times the number of initial present.


Find the equation of the curve which passes through the point (1, 2) and the distance between the foot of the ordinate of the point of contact and the point of intersection of the tangent with x-axis is twice the abscissa of the point of contact.


The slope of a curve at each of its points is equal to the square of the abscissa of the point. Find the particular curve through the point (−1, 1).


Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C2.


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


The equation of the curve whose slope is given by \[\frac{dy}{dx} = \frac{2y}{x}; x > 0, y > 0\] and which passes through the point (1, 1) is


What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?


y2 dx + (x2 − xy + y2) dy = 0


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

`y=sqrt(a^2-x^2)`              `x+y(dy/dx)=0`


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

The differential equation of y = Ae5x + Be–5x is


Solve the differential equation xdx + 2ydy = 0


Solve the following differential equation y log y = `(log  y - x) ("d"y)/("d"x)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×