In: Advanced Math

What is a Bessel Differential Equation? Classify Bessel Equation with respect to its order, linearity and homogeneity. How many independent solutions of Bessel Differential equation are needed to construct general solution?

Solve the following problems.
a) What is the order of the differential equation ? ′ = ? 2 − 3?
− 10? Is it linear ?
b) Determine whether the differential equation ? ′ = ? 2 − 3? −
10 possesses constant solutions. If yes find these constant
solutions.
c) Find the value(s) of ? so that the function ? = ? ?? is a
solution of ? ′′ − 3? ′ − 10? = 0.
Do you think...

1. What is a differential?
2. What is a differential equation?
3. Besides the fact that you might need the course to graduate, how might differential equations be useful to you in real life?

Write the second order differential equation as a system of two
linear differential equations then solve it.
y" + y' - 6y = e^-3t y(0) =0 y'(0)=0

A 2nd order homogeneous linear differential equation has
odd-even parity. Prove that if one of its
solutions is an even function and the other can be constructed as
an odd function.

Prove that for an nth order differential equation whose
auxiliary equation has a repeated complex root a+bi of multiplicity
k then its conjugate is also a root of multiplicity k and that the
general solution of the corresponding differential equation
contains a linear combination of the 2k linearly independent
solutions
e^(ax)cos(bx),
xe^(ax)cos(bx), x^2e^(ax)cos(bx),..., x^(k-1)e^(ax)cos(bx)
e^(ax)sin(bx), xe^(ax)sin(bx), x^2e^(ax)sin(bx),...,
x^(k-1)e^(ax)sin(bx)

1. Give an example of a 3rd order nonlinear ordinary
differential equation.

Solve the differential equation with details explaination :
x²y" + 6xy' - 24y=x^9

Find y(0.5) for y′=-2x-y, x0=0,y0=-1, with step length 0.1 using Euler method (1st order derivative)

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

Question 16:
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 − 11.y = 9
(a)
y = Ae -3.3.x + Be 3.3.x + 0.82
(b)
y = Ae -3.3.x + Be 3.3.x - 0.82
(c)
y = e3.3.x (Ax + B)+0.82
(d)
y = e3.3.x (Ax + B)- 0.82
Question 17:
What is the general solution of the following homogeneous second
order differential equation?
d^2y/dx^2 + 3dy/dx −...

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