Question: Check by differentiation that y = 2 cos 2t + 3 sin 2t is a solution to y + 4y = 0 by finding the

Check by differentiation that y = 2 cos 2t + 3 sin 2t is a solution to y" + 4y = 0 by finding the terms in the sum: y" Variable y' is not defined in 4y = this context So y" + 4y = 0Suppose c = est a. Find the value of the expression x" - 15x" + 75x' - 125x in terms of the variable t. (Enter the terms in the order given.) help (formulas) b. Simplify your answer to the previous part and enter a differential equation in terms of the dependent variable x satisfied by a = est. Enter the derivatives of x using prime notation ( help (formulas) c. Is x = et a solution to your differential equation in the previous part? Choose Be sure you can justify your answer.If y = est is a solution to the differential equation 8 dy + ky = 0, Variable 'y' is not defined in dt2 dt this context find the value of the constant k and the general solution to this equation. k = y= (Use constants A, B, etc., for any constants in your solution formula.)

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