9. Assume that the motion of a mass-spring system with damping is governed by dy dy + 26 + 25y = 0, y(0) =1, y/(0) = 0. dt2 dt Solve the equation of motion for y(t) and sketch the graph of y for the case in which b = 5.

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A:

Q: t^2 y^′′+aty^′+by=0, t>0 Define what type of equation is  mentioned above ?

A:

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A:

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A: The given differential equation is

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A:

Q: Solve for y(x) in paramter form: y"+7y'+10y=e^-2x

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Q: Verify that the function u=e(-α^2)t sin x is a solution of the heat conduction equation ut = α2uxx

A:

Q: find all functions u(t) that solve the equation u'(t)+t*u(t)=-t * e^(-t^2), subject to u(0) = 1

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Q: find y(t) 2.) y" + 7y' +12y = 16e^2t + t ; y(0)=6, y'(0) = 4

A:

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A:

Q: Find r(t) when r'(t)=(te^-t^2)i-(e^-t)j+k and r(0)=1/2i-j+k.

A:

Q: Find dt dt dy dx dt dt "I and 1층 x = stet y = 2t + sin(t)

A:

Q: Solve y(x) for the Second Order ODE in parameter form: y"+7y'+10y=6e^3x

A:

Q: Fnd the solution to the initial value problem: dy/dt = (2t)/(y+t^(y)), y(0) = -2

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.