differential equations

i need it in 24 hrs, correct solution with detailed steps

Show all your work neatly for full credit.

1) Solve the differential equations:

2) Compute the solution of the given initial value problem.

3) For the equation
a) determine the frequency of the beats.

b) determine the frequency of the rapid oscillations.

c) Use the informayion from parts a) and b) to give a rough sketch of the graph of a typical solution.

4) Consider the equation
a) Compute the general solution.

a)
Solve the initial value problem

5) Consider the system

a) Compute the eigenvalues

b) For each eigenvalue, compute the associated eigenvectors.

c) Using HPGSystemSolver, sketch the direction field for the system,and plot the straight-line solutions. Plot the phase portrait.

d) For each eigenvalue, specify the corresponding straight-line solution, plot its x(t) and y(t) graphs.

e) Find the general solution of the system.

f) Find the equilibrium points of the system.

g) Find the solution that satisfies the initial condition (x0, y0)=(2,1).

6) Consider the system

a) Compute the eigenvalues

b) For each eigenvalue, compute the associated eigenvectors.

c) Using HPGSystemSolver, sketch the direction field for the system,and plot the straight-line solutions. Plot the phase portrait.

d) For each eigenvalue, specify the corresponding straight-line solution, plot its x(t) and y(t) graphs.

e) Find the general solution of the system.

f) Find the equilibrium points of the system.

g) Find the solution that satisfies the initial condition (x0, y0)=(1,-1).

h) Is the origin a spiral source, spiral sink, or center.

d) d
2y
dt2

+ 6 dy
dt
+8y = 2 cos(3t), y(0) = y’ (0) = 0.

d)
d
2
y
dt
2
+6
dy
dt
+8y=2cos(3t), y(0)=y
‘
(0)=0.

a) d
2y
dt2

+ 4y = 3cos(t), y(0) = y’ (0) = 0.

a)
d
2
y
dt
2
+4y=3cos(t), y(0)=y
‘
(0)=0.

b) d
2y
dt2

+ 4y = 3cos(2t), y(0) = y’ (0) = 0.

b)
d
2
y
dt
2
+4y=3cos(2t), y(0)=y
‘
(0)=0.

d2y
dt2

+11y = 2cos(3t)

d
2
y
dt
2
+11y=2cos(3t)

d2y
dt2

+9y = cos(4t)+sin(t)

d
2
y
dt
2
+9y=cos(4t)+sin(t)

y(0) = y’ (0) = 0.

y(0)=y
‘
(0)=0.

dx
dt
= 4x−2y

dy
dt
= x+ y

dx
dt
=4x-2y
dy
dt
=x+y

dx
dt
= x+4y

dy
dt
= −3x+2y

dx
dt
=x+4y
dy
dt
=-3x+2y

a) d
2y
dt2

+ 4 dy
dt
+ 3y = 0, y(0) = 0, y’ (0) =1.

a)
d
2
y
dt
2
+4
dy
dt
+3y=0, y(0)=0,y
‘
(0)=1.

b) d
2y
dt2

+ 6 dy
dt
+8y = 0, y(0) = 0, y’ (0) =1.

b)
d
2
y
dt
2
+6
dy
dt
+8y=0, y(0)=0,y
‘
(0)=1.

c) d
2y
dt2

+ 4 dy
dt
+ 3y = e−2t, y(0) = y’ (0) = 0.

c)
d
2
y
dt
2
+4
dy
dt
+3y=e
-2t
, y(0)=y
‘
(0)=0.
Show all your work neatly for full credit.

1)

Solve the differential equations:

a
)

d
2
y
d
t
2
�
4
d
y
d
t
�
3
y
�
0
,

y
(
0
)
�
0
,
y
‘
(
0
)
�
1
.

b
)

d
2
y
d
t
2
�
6
d
y
d
t
�
8
y
�
0
,

y
(
0
)
�
0
,
y
‘
(
0
)
�
1
.

c
)

d
2
y
d
t
2
�
4
d
y
d
t
�
3
y
�
e
�
2
t
,

y
(
0
)
�
y
‘
(
0
)
�
0
.