Differential Equations Answers

Many scientists believe that large asteroid struck the earth that kill off dinosaurs. Fragment of asteroid had found out and contain 86% of its original uranium-238. How old is the fragment of the asteroid? The half-life of uranium-238 is 4.5 billion years

A radioactive substance plutonium-239 has a half-life of 24,000 years. Initially, there is 700 mg of the substance. How long for the substance to decay 78% of its initial mass?

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