ISRO Mechanical & Aerospace 2010 - Question 80

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The differential equation satisfying $y = Ae^{3x} + Be^{2x}$ is

  • A. $d^2y/dx² + 5dy/dx - 6y = 0$
  • B. $d^2y/dx² - 5dy/dx + 6y = 0$
  • C. $d^2y/dx² + 5dy/dx + 6y = 0$
  • D. $d^2y/dx² - 5dy/dx - 6y = 0$

Answer: B. $d^2y/dx² - 5dy/dx + 6y = 0$

Explanation: Roots are 3 and 2. Equation is $(D-3)(D-2)y = (D² - 5D + 6)y = 0$.

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