Constant coefficient second order equations Quiz

1. Find the complementary function of $y''-7y'+12y=0$.

• A. $Ae^{-3x}+Be^{-4x}$
• B. $Ae^{3x}+Be^{4x}$
• C. $(A+Bx)e^{3x}$
• D. $e^{3x}(A\cos4x+B\sin4x)$

2. Find the general solution of $y''-4y'+4y=0$.

• A. $Ae^{2x}+Be^{-2x}$
• B. $Ae^{2x}+B$
• C. $Ae^{2x}+Be^{4x}$
• D. $(A+Bx)e^{2x}$

3. Find the complementary function of $y''+2y'+10y=0$.

• A. $e^{-x}(A\cos3x+B\sin3x)$
• B. $e^{-x}(A\cos x+B\sin x)$
• C. $Ae^{-x}+Be^{-10x}$
• D. $e^{3x}(A\cos x+B\sin x)$

4. What trial particular integral is suitable for $y''-3y'+2y=e^{3x}$?

• A. $\lambda xe^{3x}$
• B. $\lambda e^{-3x}$
• C. $\lambda e^{3x}$
• D. $\lambda e^{x}$

5. Which trial particular integral is needed for $y''+4y=\sin2x$?

• A. $p\cos2x+q\sin2x$
• B. $x(p\cos2x+q\sin2x)$
• C. $pe^{2x}$
• D. $p\sin2x$