Exercise · ZW-CHARACTERISTIC-EQUATION-007 · ★★☆ Intermediate
An equation \(y''+by'+cy=0\) has characteristic roots \(1\) and \(-4\). Which equation is it?
Choose one option.
Show answer
- D. \(y''+3y'-4y=0\)
Explanation
\((r-1)(r+4)=r^2+3r-4\). The coefficients are the sign-changed sum (\(-(1-4)=3\)) and the product (\(-4\)) of the roots.
Review the concept: Characteristic equation
The characteristic equation of \(ay''+by'+cy=0\), with constant coefficients \(a,b,c\), is the algebraic equation in the unknown \(r\) that results from trying \(y=e^{rt}\).
\[ar^2+br+c=0\]
More practice problems: characteristic equation
- ZW-CHARACTERISTIC-EQUATION-001 What is the characteristic equation of y''-5y'+6y=0?
- ZW-CHARACTERISTIC-EQUATION-002 Solve y''-y'-6y=0.
- ZW-CHARACTERISTIC-EQUATION-003 Solve y''+4y=0.
- ZW-CHARACTERISTIC-EQUATION-004 Solve y''+2y'+y=0.
- ZW-CHARACTERISTIC-EQUATION-005 What are the roots of the characteristic equation of y''-4y=0?
- ZW-CHARACTERISTIC-EQUATION-006 Solve y''+2y'+5y=0.
- ZW-CHARACTERISTIC-EQUATION-008 For which values of b does y''+by'+9y=0 have a double characteristic root?
- ZW-CHARACTERISTIC-EQUATION-009 Solve y''-3y'+2y=0 with y(0)=1, y'(0)=0.
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