Question

dy/dt - 2y = 7e^(2t)

a. Determine the general solution to the associated homogeneous equation.

b. By choosing an appropriate guess, determine a particular solution to this differential equation.

c. Using your answers from parts (a) and (b), write down the general solution to the original equation

d. Check that your solution is correct by plugging it into the original ODE.

e. Determine the specific solution corresponding to the initial condition y(0)= 3

Pls explain how you did it

Answer #1

find the general solution of the differential equation dy/dt -
2y = t^2 * e^2t

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

4. Find a particular solution, and the general solution to the
associated homogeneous equation, of the following differential
equations:
a) y'-2y=6
b) y'+y=3e-t

Consider the differential equation. Find the solution y(0) =
2.
dy/dt = 4t/2yt^2 + 2t^2 + y + 1

Find the general solution to the differential equation y′′+ 2y′=
3 + 4 sin 2t.(Hint: Variation of parameters requires integration by
parts, so undetermined coefficientsis recommended—however, be
careful.)

Question 11:
What is the general solution of the following homogeneous
second-order differential equation?
d^2y/dx^2 + 10 dy/dx + 25.y =0
(a)
y = e 12.5.x (Ax + B)
(b)
y = e -5.x (Ax + B)
(c)
y = e -10.x (Ax + B)
(d)
y = e +5.x (Ax + B)
Question 12:
What is the general solution of the following homogeneous
second-order differential equation?
Non-integers are expressed to one decimal place.
d^2y/dx^2 − 38.y =0
(a)
y...

Find the general solution to the given differential
equation. 1+(1+ty)e^ty+(1+t^2e^ty) dy/dt=0

Determine the general solution of the given differential
equation.
y(4) − y =
2t + cos t

Consider the differential equation dy/dx= 2y(x+1)
a) sketch a slope field
b) Show that any point with initial condition x = –1 in the 2nd
quadrant creates a
relative minimum for its particular solution.
c)Find the particular solution y=f(x)) to the given differential
equation with
initial condition f(0) = 2
d)For the solution in part c), find lim x aproaches 0
f(x)-2/tan(x^2+2x)

Given y1(t)=t^2 and y2(t)=t^-1 satisfy the corresponding
homogeneous equation of
t^2y''−2y=2−t3, t>0
Then the general solution to the non-homogeneous equation can be
written as y(t)=c1y1(t)+c2y2(t)+yp(t)
yp(t) =

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