Differential Equations Answers

Determine the unique solution of the initial value problem. 

1. y′′ −2y′ +y=0,y(0)=7,y′(0)=4.

 Show that the functions 1, cos2 x, sin2 x are linearly dependent .

. The radioactive isotope carbon-10 has a half-life of 20 seconds.

a. How much time is required so that only 1/16 of the original amount remains?

b. Find the rate of decay at this time.

x(dy)/(dx)=x^(2) + 5y

x(dy)/(dx)=x^(2) + 5y

(D+2)x-3y=1

-3x+(D+2)y=e^-t

y"+3y'+2y=e^(-t) , y(0)=0, y'(0)=0

Determine the unique solution of the following differential equations by using Laplace transforms:

y''(t) + 2y'(t) -3y(t) = e^-3t if y'(0) = 0 and y(0) = 0

Determine the unique solution of the following differential equations by using Laplace transforms:

y''(t)-6y'(t)+9y(t) = t²e^3t if y'(0) = 6 and y(0) = 2

Determine L^-1{e^s(s²-1/(s²+1)²)}