Question

Prove that

ℒ{??(?)} = −?′(?)

and by using this equation, solve the following initial value problem

??′′ + (1 − ?)?′ + ? = 0, ?(0) = 1

Answer #1

Solve the 1st-order linear differential equation using an
integrating fac-
tor. For problem solve the initial value problem. For each
problem, specify the solution
interval.
dy/dx−2xy=x, y(0) = 1

Using the method of undetermined coefficients, solve the
following Initial Value Problem.
y'' - y = (t)(e^t) ; y(0) = 0 ; y(-1) = e - 1/e
Please write clearly! Thank you!

Solve the initial-value problem for linear differential
equation
y'' + 4y' + 8y = sinx; y(0) = 1,
y'(0) = 0

Solve the following initial value problem
?′′ + 3??′ + 2? = 0, ?(0) = 1 and ?′(0) = 1
by using a power series ?0 + ?1? + ?2?2 + ?3?3 + ?4?4.

Solve the following initial value problem
?′′ + 9? = 10?−?, ?(0) = 0 and ?′(0) = 0
by using the Laplace transform method.

Solve the initial value problem using Laplace transforms y "+
2ty'-4y = 1; y (0) = y '(0) = 0.

Use the Laplace transform to solve the following initial value
problem:
y′′ + 8y ′+ 16y = 0
y(0) = −3 , y′(0) = −3
First, using Y for the Laplace transform of y(t)y, i.e., Y=L{y(t)},
find the equation you get by taking the Laplace transform of the
differential equation
__________________________ = 0
Now solve for Y(s) = ______________________________ and write the
above answer in its partial fraction decomposition, Y(s) = A /
(s+a) + B / ((s+a)^2)
Y(s) =...

For the initial value problem
• Solve the initial value problem.
y' = 1/2−t+2y withy(0)=1

Solve the initial value problem below using the method of
Laplace transforms.
ty'' - 4ty' + 4y = 8, y(0) = 2, y'(0) = -5

Solve the following initial value problems using MATLAB’s
dsolve command, (write the coding used for the
problem using the dsolve command and I will do the
rest, I just can't get the coding right)
y' = 2y(3 - y), for different initial conditions, y(0) = 4, y(0)
= 2, y(0) = -1

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