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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

State whether the following statement is True or False: The integrating factor of the differential equation dydx-y = x is e–x - Mathematics and Statistics

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प्रश्न

State whether the following statement is True or False:

The integrating factor of the differential equation `("d"y)/("d"x) - y` = x is e–x 

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

True

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.8: Differential Equation and Applications - Q.3

संबंधित प्रश्‍न

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


\[\frac{dy}{dx} = x^5 + x^2 - \frac{2}{x}, x \neq 0\]

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

\[x\frac{dy}{dx} + 1 = 0 ; y \left( - 1 \right) = 0\]

xy dy = (y − 1) (x + 1) dx


\[xy\frac{dy}{dx} = y + 2, y\left( 2 \right) = 0\]

\[\frac{dy}{dx} = y \tan x, y\left( 0 \right) = 1\]

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

\[2\left( y + 3 \right) - xy\frac{dy}{dx} = 0\], y(1) = −2

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

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

A population grows at the rate of 5% per year. How long does it take for the population to double?


In a simple circuit of resistance R, self inductance L and voltage E, the current `i` at any time `t` is given by L \[\frac{di}{dt}\]+ R i = E. If E is constant and initially no current passes through the circuit, prove that \[i = \frac{E}{R}\left\{ 1 - e^{- \left( R/L \right)t} \right\}.\]


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


Choose the correct option from the given alternatives:

The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is


In the following example, verify that the given function is a solution of the corresponding differential equation.

Solution D.E.
y = xn `x^2(d^2y)/dx^2 - n xx (xdy)/dx + ny =0`

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

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


Solve: `("d"y)/("d"x) + 2/xy` = x2 


Choose the correct alternative:

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


If `y = log_2 log_2(x)` then `(dy)/(dx)` =


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