Exercise · ZW-SOLUTION-OF-A-DIFFERENTIAL-EQUATION-005 · ★★☆ Intermediate
For which value of \(k\) is \(y=e^{kx}\) a solution of \(y''-5y'+6y=0\)?
Choose one option.
Show answer
- C. 2
Explanation
Substituting gives \((k^2-5k+6)e^{kx}=0\), that is \(k=2\) or \(k=3\). Among the options, only \(k=2\).
Review the concept: Solution of a differential equation
A solution \(\varphi\) of a differential equation \(F=0\) is a function that, substituted together with its derivatives, makes the equation a true identity on a whole interval.
\[F\big(x,\varphi(x),\varphi'(x),\dots,\varphi^{(n)}(x)\big)=0\]
More practice problems: solution of a differential equation
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- ZW-SOLUTION-OF-A-DIFFERENTIAL-EQUATION-006 For which value of k is y=sin (kx) a solution of y''+9y=0?
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- ZW-SOLUTION-OF-A-DIFFERENTIAL-EQUATION-008 Which equation does y=xln x (with x>0) satisfy?
- ZW-SOLUTION-OF-A-DIFFERENTIAL-EQUATION-009 The function y=(1)/(1-x) satisfies y'=y^2. On which interval is it a solution?
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