Find the power series in x for the general solution of (1+x^2)y"+6xy'+6y=0. Please show all your work step by step.

Find the power series in x for the general solution of (1+x^2)y"+6xy'+6y=0. Please show all your work step by step.

Find the power series in x for the general solution of (1+x^2)y"+6xy'+6y=0. Here's my work: Ly=(1+x^2)y"+6xy'+6y y=Σanxn from n=0...

Solve the differential equation xy' = y + xe^(9y/x) by making the change of variable v = y/x. Please help and show your work! Thanks in advance!

solve the difference equation x_{n+2} - 4x_{n}= n with initial conditions: x_{0} = 0, x_{1} = 1/3

Assume that there's no damping, an object stretches a spring 4 inches in equilibrium. Find its displacement for t>0 if it's initially displaced 36 inches above equilibrium and given a downward...

A 64 lb object stretches a spring 4 ft in equilibrium. It is attached to a dashpot with damping constant c=8 lb-sec/ft. The object is initially displaced 18 inches above equilibrium and given a downward...

A weight stretches a spring 1.5 inches in equilibrium. The weight is initially displaced 8 inches above equilibrium and given a downward velocity of 4 ft/s. Find its displacement for t>0. y"+(k/m)y=0 I...

An object stretches a spring 5 cm in equilibrium. It is initially displaced 10 cm above equilibrium and given an upward velocity of 0.25 m/s. Find its displacement for t>0. Find the frequency,...

A spring with natural length 0.5 m has length 50.5 cm with a mass of 2 gm suspended from it. The mass is initially displaced 1.5 cm below equilibrium and released with zero velocity. Find its displacement...

Hello, I've got some problems solving general and particular solutions of differential equations. I hope to understand how they work, if you could help me with a detailed solution for these...

I need help answering this word problem...I need to find the function P(t) and I just can't remember the process whatsoever "A company has its profit function P(t) defined since...

Which method do we use and what are the steps?

Let r=6x5/4,x>0. Use differentials to estimate the percentage change in r, if x increases by 4 . What is the percentage change in r?

Hello, I'm having difficulties, generally, with solving problems with differential equations. I hope to see a pattern and find solutions eventually myself by having detailed solutions...

A very large tank initially contains 15 gallons of saltwater containing 6 pounds of salt. Saltwater containing 1 pound of salt per gallon is pumped into the top of the tank at a rate of 2 gallons...

a. dy/dt = 2y-t b. dy/dt=3y+2t Please explain and show all working. Thank you ;)

Find the initial guess for y"+y=xe^(x). And show your work.

Find the initial guess for y"-6y'+10y=-e^(3x)(6cosx+4sinx).

Find a particular solution of y"-2y'+2y=e^(x)[(2-2x-6x^2)cosx+(2-10x+6x^2)sinx]. How to find the correct initial guess for this problem?

Find a particular solution of y"-2y'+y=-e^(x)[(3+4x-x^2)cosx+(3-4x-x^2)sinx]. I need to do this problem by the method of undetermined coefficients. What's the correct...

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