Question

Consider the initial value problem

*y'* +

5 |

4 |

*y* = 1 −

t |

5 |

, *y*(0) =
*y*_{0}.

Find the value of

*y*_{0}

for which the solution touches, but does not cross, the
*t*-axis. (A computer algebra system is recommended. Round
your answer to three decimal places.)

*y*_{0} =

Answer #1

Consider the initial value problem: y' - (7/2)y = 7t + 2e^t
Initial condition: y(0) = y0
a) Find the value of y0 that separates
solutions that grow positively as t → ∞ from those that
grow negatively. (A computer algebra system is recommended. Round
your answer to three decimal places.)
b) How does the solution that corresponds to this critical value
of y0 behave as t → ∞?
Will the corresponding solution increase without bound, decrease
without bound, converge...

Consider the initial value problem 4u'' − u' + 2u = 0, u(0) = 5,
u'(0) = 0. (a) Find the solution u(t) of this problem. u(t) = (b)
For t > 0, find the first time at which |u(t)| = 10. (A computer
algebra system is recommended. Round your answer to four decimal
places.) t = Show My Work (Optional)

1-Consider the following.
36y'' − y = 0,
y(−4) = 1, y'(−4) = −1
Find the solution of the given initial value problem.
y(t) = ?
2- Consider the vibrating system described by the initial value
problem. (A computer algebra system is recommended.)
u'' + u = 9 cos ωt,
u(0) = 5, u'(0) = 4
3-A spring is stretched 6 in. by a mass that weighs 8 lb. The
mass is attached to a dashpot mechanism that has a...

Find the solution to the initial value problem
(y′−e−t+5)/y=−5, y(0)=−4
Discuss the behavior of the solution y(t)y(t) as tt becomes
large. Does limt→∞y(t)limt→∞y(t) exist? If the limit exists, enter
its value. If the limit does not exist, enter DNE.

Find the solution to the initial value problem
(y′−e−t+5)/y=−5, y(0)=−4
Discuss the behavior of the solution y(t)y(t) as tt becomes
large. Does limt→∞y(t)limt→∞y(t) exist? If the limit exists, enter
its value. If the limit does not exist, enter DNE.

Consider the following Initial Value Problem (IVP)
y' = 2xy, y(0) = 1.
Does the IVP exists unique solution? Why? If it does, ﬁnd the
solution by Picard iteration with y0(x) = 1.

B1. Consider the initial value problem given by y 0 (t) = sin2
(y) ln(t + 1), with the initial condition y(0) = 1. Perform three
iterations of Midpoint Method, using a step size of h = 1 3 , to
obtain an estimate of the solution at t = 1.

Consider the following. (A computer algebra system is
recommended.)
y' = 3x/(y+x^2y')
(a) Find the solution of the given initial value problem in
explicit form.
y' = 3x/(y+x^2y')
y(0)=-6
question asks for answer in terms of y(x)=
(b) Plot the graph of the solution.

2. Find the solution of the initial value problem y''−y=0, y(0)
= 5/4, y'(0) =−3/4.

Find the solution of the given initial value problem.
ty′+3y=t2−t+5, y(1)=5, t>0

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