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Differential equations

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See attached

(1) Write the general solution for: x2 y" - 2xy+2y=x3

(2) Solve:

(3) Solve: x2 y" + xy' - y=0

(4) Calculate L[x sinax]

(5) In the vibration of a mass-spring-damper system, the displacement is governed by

If f(t) is given by

Find the solution if C=0 and

x(t=0)=0 and dx/dt(t=0)=0

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Solution Summary

This provides examples of working with differential equations, including spring-damper problem.

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Hello

Please find the solution in the attached file.

(1) Write the general solution for: x2 y" - 2xy+2y=x3

For this equation

Let then our equation convert into

For Complementary Solution

Auxiliary equation is

Then
C. F. =

And

Then solution

Or

...

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