Question

Find a particular solution to the following equations

(d'''y/dt''') + y = t^3 + sint + 11e^t

(d'' y/dt'') + y = 2tsint

(d'''''y/dt''''') − (4d'''y/dt''') = e^2t + t^2 + 5t + 4

Answer #1

3. For each of the following equations find a particular
solution yp(t).
(a) y"+4y= e^(5t)
(b) 4y"+4y'+y = 3t(e^t)
(c) y"+4y'+2y=t^2
(d) y"+9y = cos(3t) +4sin(3t)

(1 point) Match the following nonhomogeneous linear equations
with the form of the particular solution yp for the method of
undetermined coefficients.
? A B C D
1. y′′+y=t(1+sint)
? A B C D
2. y′′+4y=t2sin(2t)+(5t−7)cos(2t)
? A B C D
3.
y′′+2y′+2y=3e−t+2e−tcost+4e−tt2sint
? A B C D
4.
y′′−4y′+4y=2t2+4te2t+tsin(2t)
A.
yp=t(A0t2+A1t+A2)sin(2t)+t(B0t2+B1t+B2)cos(2t)
B.
yp=A0t2+A1t+A2+t2(B0t+B1)e2t+(C0t+C1)sin(2t)+(D0t+D1)cos(2t)
C.
yp=Ae−t+t(B0t2+B1t+B2)e−tcost+t(C0t2+C1t+C2)e−tsint
D. yp=A0t+A1+t(B0t+B1)sint+t(C0t+C1)cost

Using variation of parameters, find a particular solution of the
given differential equations:
a.) 2y" + 3y' - 2y = 25e-2t (answer should be: y(t) =
2e-2t (2e5/2 t - 5t - 2)
b.) y" - 2y' + 2y = 6 (answer should be: y = 3 + (-3cos(t) +
3sin(t))et )

Find the general solution of the equation.
d^2y/dt^2-2t/(1+t^2)*dy/dt+{2/(1+t^2)}*y=1+t^2

Consider the differential equation y”+5y’+6y=f(t). Write the
form of the particular solution if f(t) is the following. Do not
solve.
(a) f(t)= 5t*e^(-2t)
(b) f(t)= t^2*sin(2t)
(c) f(t)= t + 1
(d) f(t)= 2t^2*e^(-3t)
(e) f(t)= 4t^2+3t

Consider the differential equation y”+5y’+6y=f(t). Write the
form of the particular solution if f(t) is the following. Do not
solve.
(a) f(t)= 5t*e^(-2t)
(b) f(t)= t^2*sin(2t)
(c) f(t)= t + 1
(d) f(t)= 2t^2*e^(-3t)
(e) f(t)= 4t^2+3t

Use undetermined coefficients to find the particular solution
to
1) y''−2y'+3y= 5t^2+2t+2
yp(t)=?
2) y''+y'−20y= −2550sin(3t)
yp(t)=?

Find a Particular Solution of
y'''-4y'=t+3cos(t)+e-2t

For problem 1 to 3, use r(t)= <e^2t cost, e^2t sint, e^2t>
to find each of the following at t = 0.
1, T(t)
2, N(t)
3, Curvature

Find the general solution to the following:
[(e^t)y-t(e^t)]dt+[1+(e^t)]dy=0

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