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

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प्रश्न

Choose the correct alternative.

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

विकल्प

  • 4 hours

  • 6 hours

  • 8 hours

  • 10 hours

MCQ
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उत्तर

Bacteria increases at the rate proportional to the number present. If the original number M doubles in 3 hours, then the number of bacteria will be 4M in 6 hours

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Differential Equation and Applications - Miscellaneous Exercise 8 [पृष्ठ १७२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 1.08 | पृष्ठ १७२

संबंधित प्रश्न

\[\frac{d^3 x}{d t^3} + \frac{d^2 x}{d t^2} + \left( \frac{dx}{dt} \right)^2 = e^t\]

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

Show that y = e−x + ax + b is solution of the differential equation\[e^x \frac{d^2 y}{d x^2} = 1\]

 


For the following differential equation verify that the accompanying function is a solution:

Differential equation Function
\[x\frac{dy}{dx} + y = y^2\]
\[y = \frac{a}{x + a}\]

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


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

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

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

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

(y + xy) dx + (x − xy2) dy = 0


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

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

(x + y) (dx − dy) = dx + dy


(x2 − y2) dx − 2xy dy = 0


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

\[\frac{dy}{dx} = \frac{y}{x} - \sqrt{\frac{y^2}{x^2} - 1}\]

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

 

Find the equation of the curve which passes through the origin and has the slope x + 3y− 1 at any point (x, y) on it.


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


The differential equation
\[\frac{dy}{dx} + Py = Q y^n , n > 2\] can be reduced to linear form by substituting


y2 dx + (x2 − xy + y2) dy = 0


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

Solution D.E.
xy = log y + k y' (1 - xy) = y2

Solve the following differential equation.

`dy/dx + 2xy = x`


Solve the following differential equation.

`(x + a) dy/dx = – y + a`


Choose the correct alternative.

The integrating factor of `dy/dx -  y = e^x `is ex, then its solution is


Solve the differential equation `("d"y)/("d"x) + y` = e−x 


Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`


Solve the differential equation xdx + 2ydy = 0


The solution of differential equation `x^2 ("d"^2y)/("d"x^2)` = 1 is ______


Solve the differential equation `dy/dx + xy = xy^2` and find the particular solution when y = 4, x = 1.


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