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Elementary Differential Equations Problems: 1) Find the solution of the initial value problem of y" + 3y'...

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Advance Math

Elementary Differential Equations Problems:

1) Find the solution of the initial valueproblem of y" + 3y' = 0, y(0) = -2, y'(0) = 3

2) Find the general solution of the equation4y" - 9y = 0

3) Find the general solution of the equationdy/dt = 2t(y – 2y2)

4) Given the second order linear homogeneousequation y"- 2y' + y = 0,

a) Verify that y1(t) = e^t andy2(t) = t e^t are solutions of the equation

b) Compute the Wronskian of y1, y2

c) Would y(t) = C1y1(t) +C2y2(t) also be a solution to the equationfor arbitrary constants C1,C2? Explain.

5) Consider the second order non-lineardifferential equation (y * y") + (y’)2 = 0 for t >0

a) Verify that y1(t) = 1 and y2(t) =t1/2 are solutions of this equation

b) Let y(t) = C1y1(t) +C2y2(t) = C1+ (C2 *t1/2), for constants C1,C2.Compute y' and y"

c) Use the results from above to show that y(t) isNOT always a solution of the equation (y * y") +(y’)2 = 0 for all C1, C2

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