Question

y”+6y’+9y=e^-3t

Answer #1

Solve the second order differential equation
y'' + 6y' + 9y = e^(-3t) + t^(3)

use
the laplace transform to solve the following equation
y”-6y’+9y = (t^2)(e^(3t))
y(0)=2
y’(0)=17

Find the general solution to y''+6y'+9y=e^-3x

Consider the second-order homogeneous linear equation
y''−6y'+9y=0.
(a) Use the substitution y=e^(rt) to attempt to find two
linearly independent solutions to the given equation.
(b) Explain why your work in (a) only results in one linearly
independent solution, y1(t).
(c) Verify by direct substitution that y2=te^(3t) is a solution
to y''−6y'+9y=0. Explain why this function is linearly independent
from y1 found in (a).
(d) State the general solution to the given equation

Solve the initial value problem y′′+6y′+9y=0, y(−1)=3,
y′(−1)=3.

4. Find a general solution of y" + 9y = 18e^(−t) cos(3t).

Solve the given initial-value problem.
y''' + 6y'' +
9y' = 0, y(0) = 0,
y'(0) = 1, y''(0) = −6

Find the general solution of the equation: y''+6y'+9y=0 where
y(1)=3 y' (1)=-2 and then find the particular solution.

Find the general solution of the differential equation
y′′+9y=11sec2(3t), 0<t<π6.

Find the particular solution to y′′+9y=6sec(3t). Do not include
the complementary solution yc=C1y1+C2y2. y=

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