Advertisements
Advertisements
Question
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
Options
4 hours
6 hours
8 hours
10 hours
Solution
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
APPEARS IN
RELATED QUESTIONS
Verify that \[y = e^{m \cos^{- 1} x}\] satisfies the differential equation \[\left( 1 - x^2 \right)\frac{d^2 y}{d x^2} - x\frac{dy}{dx} - m^2 y = 0\]
(1 + x2) dy = xy dx
tan y dx + sec2 y tan x dy = 0
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
\[\frac{dy}{dx} = \frac{y}{x} + \sin\left( \frac{y}{x} \right)\]
The normal to a given curve at each point (x, y) on the curve passes through the point (3, 0). If the curve contains the point (3, 4), find its equation.
Write the differential equation obtained by eliminating the arbitrary constant C in the equation x2 − y2 = C2.
The solution of the differential equation \[\frac{dy}{dx} - \frac{y\left( x + 1 \right)}{x} = 0\] is given by
If a + ib = `("x" + "iy")/("x" - "iy"),` prove that `"a"^2 +"b"^2 = 1` and `"b"/"a" = (2"xy")/("x"^2 - "y"^2)`
Find the equation of the plane passing through the point (1, -2, 1) and perpendicular to the line joining the points A(3, 2, 1) and B(1, 4, 2).
Find the differential equation whose general solution is
x3 + y3 = 35ax.
Solve the following differential equation.
(x2 − y2 ) dx + 2xy dy = 0
Choose the correct alternative:
Solution of the equation `x("d"y)/("d"x)` = y log y is
A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution
The function y = cx is the solution of differential equation `("d"y)/("d"x) = y/x`
Given that `"dy"/"dx"` = yex and x = 0, y = e. Find the value of y when x = 1.
`d/(dx)(tan^-1 (sqrt(1 + x^2) - 1)/x)` is equal to:
