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Diff Eq 3.50

 

<== Differential Equations
Number Question Answer
See the work
1. Use the method of undetermined coefficients to find one solution of
y''  - 9y'  + 9y  =  5 e^{8 t}.

y=
5e^(8t)+e^((9-sqrt(45))/2t)+e^((9-sqrt(45))/2t)
The work

Point Cost: 3
2. Find a particular solution to the differential equation
-6 y''  - 5 y'  - 1 y = -1 t^2 + 1 t  - 1 e^{4 t} .

y_{p} =
t^2+(-11t)+43+1/117e^(4t)
The work

Point Cost: 3
3. Find a particular solution to
y''  - 4 y' + 4 y =  14.5 e^{2 t}.

y_{p} =
29/4t^2e^(2t)
The work

Point Cost: 3
4. Find a particular solution to the differential equation
y''  - 4 y'  - 5 y = 25 t^3 .

y_{p} =
(-5t^3+12t^2-(126/5)t+624/25)
The work

Point Cost: 3
5. Find a particular solution to
y'' + 5 y' + 4 y =  11 t e^{5 t} .

y_{p} =
(11/54t-55/972)e^(5t)
The work

Point Cost: 3
6. Find the solution of
y'' + 2y'   - 8y  =  32 \,e^{4 t}
with y(0)=4 and y'(0)=5.
y =
(5/6)e^(2t)+(7/6)e^(-4t)+2e^(4t)
The work

Point Cost: 3
7.
Find the solution of

y'' + 5y'  =  250 \,\sin(5 t) + 450 \, \cos(5 t)

with y(0) = 4 and y'(0) = 2
y = 
72/5+(18/5)e^(-5t)-14cos(5t)+4sin(5t)
The work

Point Cost: 3
8. Find a particular solution to
y'' +  16 y =  -16 \sin(4 t) .

y_{p} =
2tcos(4t)
The work

Point Cost: 3
9. Find y as a function of x if
y'''- 13 y'' + 36 y' =  120 e^x,
y(0) = 12, \ \ y'(0) = 30, \ \ y''(0) = 26.
y(x)=
-13/9-79/45e^(9x)+51/5e^(4x)+5e^x
The work

Point Cost: 3