ISRO Mechanical & Aerospace 2011 - Question 73

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General solution of the differential equation $(D² - 2D + 1)y = e^x$ is

  • A. $Ae^x + Be^{-x} + x² e^x / 2$
  • B. $e^x (A + Bx) - x² e^x / 2$
  • C. $Ae^x + Be^{-x} - x² e^x / 2$
  • D. $e^x (A + Bx) + x² e^x / 2$

Answer: D. $e^x (A + Bx) + x² e^x / 2$

Explanation: Roots are 1,1 (repeated). CF is $(A+Bx)e^x$. PI for $e^x$ with $(D-1)^2$ involves $x²/2!$.

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