Consider the differential equation x′=[2 4
-2 −2],
with x(0)=[1 1]
Solve the differential equation where x=[x(t)y(t)].
x(t)=
y(t)=
please be as clear as possible especially when solving for c1
and c2 that's the part i need help the most
consider the autonomous diffeerential equation y'=(y-4)(y+2)
1) what are the constant solutions of this differential
equation?
2) Let g(y)=(y-4)(y+2) sketch this curve with y on the
horizontal axis
3) for which of the following inital conditions. is the
solution curve incrreasing y(0)=-3, y(0)=2, y(0)=5
4) Plot the solution curves corresponding to the intial
conditions in part c. in the ty plane
5) classify each of the constant solutions you found as
stable, unstable, or semi
5. Consider the differential equation
xy^5/2 +1+x^2y^3/2dy/dx =0
(a) Show that this differential equation is not exact.
(b) Find a value for the constant a such that, when you multiply
the d.e. through by xa, it becomes exact. Show your working. Do NOT
solve the resulting differential equation.
6. Consider the differential equation
(D − 3)(D − 4)y = 0.
(a) Solve this d.e., showing brief working.
(b) How many solutions does this d.e. have? Justify your
answer.
(c) How...
The differential equation representing the family of ellipse having foci either on the x axis or on the y axis centre at the origin and passing through the point (0, 3) is
Consider the differential equation
(x
2 + 1)y
′′ − 4xy′ + 6y = 0.
(a) Determine all singular points and find a minimum value for the
radius of convergence of
a power series solution about x0 = 0.
(b) Use a power series expansion y(x) = ∑∞
n=0
anx
n
about the ordinary point x0 = 0, to find
a general solution to the above differential equation, showing all
necessary steps including the
following:
(i) recurrence relation;
(ii) determination...
9. For the differential equation: ?′′ + 2?′ + 5? = ?(?)
(a) Write down the auxiliary polynomial associated to this
differential equation and find the roots of the auxiliary
polynomial.
(b) Find a basis for the real solution set of the associated
homogeneous differential equation ?′′ + 2?′ + 5? = 0.
(c) For each ?(?) that follows, write down the trial particular
solution to ?′′ + 2?′ + 5? = ?(?), with undetermined coefficients.
Do NOT solve the...
What differential equation is the one-dimensional potential
equation? What is the form of the solution of the one-dimensional
Dirichlet problem? The one-dimensional Neumann problem?