Question

Solve the given initial-value problem. d2x dt2 + 4x = −5 sin(2t) + 9 cos(2t), x(0) = −1, x'(0) = 1

Answer #1

d2x dt2 + 9x = 2 sin(3t), x(0) = 5, x'(0) = 0

Solve this Initial Value Problem using the Laplace
transform.
x''(t) - 9 x(t) = cos(2t),
x(0) = 1,
x'(0) = 3

Use the Laplace transform to solve the given system of
differential equations. d2x dt2 + d2y dt2 = t2 d2x dt2 − d2y dt2 =
3t x(0) = 8, x'(0) = 0, y(0) = 0, y'(0) = 0

Solve for −?≤?≤?.
(a) cos x – sin x = 1
(b) sin 4x – sin 2x=0
(c) cos x−√3sin ? = 1

use Laplace transformations to solve initial value problem
x''+4x=cos(t), x(0)=0, x'(0)=0
set up the appropriate form of a particular solution, do not
determine coefficients,
y''+6y'+13y=e-3x cos2x
find the Laplace transformation of the following function
f(t)=4cos(2t) + 7t3 - 5e-3t

5. Solve the initial value problem x" + 4x' = −64e^(4t) , x(0) =
2, x'(0) = 0

Solve the Initial Value Problem
(y2 cos(x) − 3x2y − 2x) dx + (2y sin(x) −
x3 + ln(y)) dy = 0, y(0) = e

Solve the following
a) 2 cos^2(4x) + 5 cos(4x) + 2 = 0.
b) arctan(3x + 3) = π/4
c) 2^1+sin^2(x) = 4^sin(x)
d) ln(x + 3) = ln(x) + ln(3)

solve the following initial value problem x' = 2xy
y' = y -2t +1 x(0) = x0 y(0) =
y0

Initial Value Problem. Use Laplace transform.
m''(t) - 9*m(t) = cos(2t)
where m(0) = 1 and m'(0) = 3

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