110年 - 110 國立臺北科技大學_碩士班招生考試_機械工程系機電整合碩士班：工程數學#107430

科目：研究所、轉學考(插大)◆工程數學 | 年份：110年 | 選擇題數：0 | 申論題數：7

試卷資訊

所屬科目：研究所、轉學考(插大)◆工程數學

選擇題 (0)

申論題 (7)

1. Use the integrating factor method to solve the following ordinary differential equation.

y'+y= (10%)

2. Solve for the following ordinary differential equation

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%)

6. Use the Laplace transform to solve the following ordinary differential equation.

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%)