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CSS Applied Mathematics QUESTION #4146
Question 1
For the ODE $y'' - 3y' + 2y = e^x$, what is the form of particular solution $y_p$ using undetermined coefficients?
  • $Ae^x$
  • $Axe^x$✔️
  • $Ax^2e^x$
  • $A\cos(x) + B\sin(x)$
Correct Answer Explanation
Characteristic equation: $r^2 - 3r + 2 = 0$ gives $r = 1, 2$. Since $e^x$ corresponds to $r=1$ (simple root), multiply by $x$: $y_p = Axe^x$.