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6. Use the Laplace transform to solve the following ordinary differential equation.
y"+4y = f(t)
y(0) =y'(0)=1

其他申論題

2. Solve for the following ordinary differential equation (15%)

3. Use the undetermined coefficient method to solve the following ordinary differential equation y" + y = cos(x) (15%)

4. Use the Lagrange method (variation parameter method) to solve the same ordinary differential equation shown in problem 3. y" +y = cos(x) (15%)

5. Using the Laplace transform to solve the following initial value ordinary differential problem. y" + 8y'+ 16y = y(0) = 1, y'(0) =-4 (15%)

7. An elastic string of length L with fixed ends is released from rest (zero initial velocity) from an initial position given as a function of y = f(x). The initial- boundary value problem for the position function y(x,t) is Please solve for the function of the position function y(x, t) (15%)

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