In: Advanced Math

Consider the following equation: (3 − x^2 )y'' − 3xy' − y = 0 Derive the general solution of the given differential equation about x = 0. Your answer should include a general formula for the coefficents.

Diff. equations
Consider the equation (x^2 − 2)y''+ 3xy'+ y = 0.
a) Find the general solution as a power series centered at x =
0. Write the first six nonzero terms of the solution. And write the
solution using sigma notation with a formula for the coefficients.
Write the two linearly independent solutions that form the general
solution.
b) Find a power series solution satisfying the initial
conditions y(0) = 2 and y' (0) = 3. Write the first...

Consider the differential equation:
y'(x)+3xy+y^2=0.
y(1)=0. h=0.1
Solve the differential equation to determine y(1.3)
using:
a. Euler Method
b. Second order Taylor series method
c. Second order Runge Kutta method
d. Fourth order Runge-Kutta method
e. Heun’s predictor corrector method
f. Midpoint method

Find two power series solutions of the given differential
equation about the point x=0
(x^2+2) y″+3xy'-y=0

solve using forbenious series
3xy''+(2-x)y'-y=0

Consider the equation x^2+(y-2)^2 and the relation “(x, y) R (0,
2)”, where R is read as “has distance 1 of”. For example, “(0, 3) R
(0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation
can also be read as “(x, y) belongs to the circle of radius 1 with
center (0, 2)”. In other words: “(x, y) satisfies this equation if,
and only if, (x, y) R (0, 2)”. Does this equation determine a...

Consider a Cauchy-Euler equation x^2y''- xy' +y =x^3 for
x>0.
a) Rewrite the equation as constant- coefficeint equation by
substituting x = e^t.
b) Solve it when x(1)=0, x'(1)=1.

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...

Solve this differential equation
y''+(-4-2-2)y'+(4+4+4+4)y=x
y(0)=3-2
y'(0)=2-3
Answer it as y(x)=... and motivate all the steps of the
calculation

Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are
all real numbers
(a) Derive an equation for a line tangent to both of these
parabolas (show all steps with a proof, assuming that such
a line exists)
(b) Assume that the doubly-tangent line has an equation y+Ax+B.
Find an example of values of a,b,c (other than the ones given here)
such that A,B ∈ Z

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1
Solve (x^3+y^3)dx+3xy^2 dy = 0
Solve (y-cos y)dx + (xsiny+x)dy = 0
Solve (1+ln x +y/x)dx = (1-lnx)dy
Solve (y^2+yx)dx - x^2dy =0
Solve (x^2+2y^2)dx = xydy
Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2)
Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2)
Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2
Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0
Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1
6. Mixture Problem
Initially 40 lb of salt is dissolved in a large...

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- What is the treatment for schzophrenia condition? How was this disorder treated in the past? Has...
- Which of these are a case for Cultural Relativism? 1. Different societal contexts demand different moral...
- Annuity You are going to borrow money from the bank. But when considering your income, you...
- As you will learn, working in groups is no easy task! Hopefully, you will master some...
- An agronomist is conducting a field experiment to identify the best management practice for minimizing spread...
- What’s a firm’s market value? What are some factors driving a firm’s market value?
- Create the following positions based upon a job analysis: Mailroom clerk: Entry level for a long-term...

ADVERTISEMENT