Search & Filtering
In 8: 00 AM, the population of a bacteria is 1000. At 11: 30 AM, the number of bacteria triples. At what time will the population become 300 times the initial population of bacteria?
A certain artifact was found in 2020 to contain presently 83% of its original carbon-14. In what year did the artifact first exist? The half-life of carbon-14 is approximate 5,740 years.
a bacteria culture is known to grow at a rate proportional to the amount present. after one hour, 1000 strands of the bacteria are observed in the culture; and after four hours, 30000 strands. Find an expression fo the approximate number of strands of the bacteria present in the culture at any time t.
solve y(2x+y-2)dx=2(x+y)dy
Find the Wronskian of the following functions and determine whether it is linearly dependent or linearly independent on (-∞,∞).
{x2, x+1, x-3} ans, W=8, linearly independent
{3e2x, e2x} ans, W=0, linearly dependent
{x2, x3, x4} ans, W=2x^6, linearly independent
[C] Solve the following differential equation:
x^ 2 y^ " - 2xy'-4y=x^ 2 +2 log x
y''-4y'+4y=(x+1)e^x
Solve this Diffrential equation (1-x^2)y"-2xy'+n(n+1)y=0 using Power Series Method
A circuit has in series an electromotive force given by E=40-sin35tV, a resistor of 10Ω, and an inductor of 0.4H . If the initial current is 2 , find the current at time t>2.
Solve the following Second Order equation with constant co-efficient
y’’ - 6y’+25 y = 0.
Solve the following second order non-homogenous equation:
y" + y = sin (2x)
Solve the following Bernoulli's initial value problem differential equation:
6y’ — 2y=xy⁴ y(0)=–2
Solve the following initial value problem equation:
2x²y" + 3xy' 15y = 0, y (1)=0 y' (1) = 1
