Mapúa Institute of Technology - Old Testaments: MATH24 - Long Quiz #3 - 2nd TERM

I. Fill in the blanks. (5 points each)

1. If the characteristic roots of f(D)y = 0 is

i, the primitive (complimentary solution) is _______________.

2. If the characteristic root of f(D)y = 0 is 2 with multiplicity of 2, the primitive is _______________.

3. If the primitive is y = C

, the differential equation is _______________.

4. The product of D(xD – 1) is equal to _______________.

II. Find y_p of the given higher-order differential equation using Inverse Operator. (15 points each)

1. (D – 2)(D – 5)y = e²^x + 3e^-5^x

2. y” + 25y = 6sin x

III. Solve the given initial-value problem. (20 points)

y” + y = 0, y

= 0, y

= 2

IV. Solve the given differential equation by variation of parameters. (20 points)

y” – y =

V. Solve the given differential equation by the method of undetermined coefficients. (20 points)

y” + 2y’ – 3y = e^x + sin x