Question

	LIST I		LIST II
A.	d²y/dx² + 13y = 0		I. ex(c1 + c2x)
B.	d²y/dx² + 4dy/dx + 5y = cosh 5x		II. e2x(c1 cos 3x + c2 sin 3x)
C.	d²y/dx² + dy/dx + y = cos²x		III. c1ex + c2e3x
D.	d²y/dx² - 4dy/dx + 3y = sin 3x cos 2x		IV. e-2x(c1 cos x + c2 sin x)

Choose the correct answer from the options given below:

• (A) - (I) (B) - (II) (C) - (III) (D) - (IV)
• (A) - (II) (B) - (III) (C) - (I) (D) - (IV)
• (A) - (III) (B) - (IV) (C) - (I) (D) - (II)
• (A) - (II) (B) - (IV) (C) - (I) (D) - (III)

Hint:

For second-order linear equations with constant coefficients, the complementary function is found by solving the characteristic equation.

Answer 1

The Correct Option is D

The complementary function for each differential equation is identified based on the form of the equation, and the solutions are matched accordingly.