110年 - 110 國立臺灣科技大學_碩士班招生試題_材料科學與工程系(乙組)：工程數學#113288

3. Solve the differential equation (15%)

4. Solve the initial value problem by using the Laplace transform. (15%)
y"-4y'+4y=f(t)；y(0)=-2,y'(0)=1, with
  

5. Please find the half-range cosine and sine expansions of the given function.(15%)

6. Please use the method of undetermined coefficients to solve the given system. (15%)

7. Evaluateds,where C is given by x=6cos(t) y=6sin(t)，0 ≤t≤2π. (10%)

8. Find a value of x which the matrix is its own inverse. (10%)