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:
| 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) |
Show Hint
For second-order linear equations with constant coefficients, the complementary function is found by solving the characteristic equation.
Updated On: Feb 11, 2026
- (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)
Show Solution
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The Correct Option is D
Solution and Explanation
The complementary function for each differential equation is identified based on the form of the equation, and the solutions are matched accordingly.
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