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Determine the unique solution of the initial value problem.
- y′′ −2y′ +y=0,y(0)=7,y′(0)=4.
Show that the functions 1, cos2 x, sin2 x are linearly dependent .
Determine all intervals on which the equation is normal.
- (tanx)y′′′+y=0
Find the Laplace transform, if it exists, of each of the following functions
(d) f(t) = et2
. 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.
Use the Bisection method to find solutions, accurate to within 10−5 for the following problems. a. 3x − ex = 0 for 1 ≤ x ≤ 2 b. 2x + 3 cos x − ex = 0 for 0 ≤ x ≤ 1 c. x2 − 4x + 4 − ln x = 0 for 1 ≤ x ≤ 2 and 2 ≤ x ≤ 4 d. x + 1 − 2 sin πx = 0 for 0 ≤ x ≤ 0.5 and 0.5 ≤ x ≤ 1
x(dy)/(dx)=x^(2) + 5y
x(dy)/(dx)=x^(2) + 5y
y "t 2y 't 3y t e3t , if y(0) 0 and y '(0) 0 .
L^-1 (11-3s/s^2 +2s-3)
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