## Related questions with answers

Question

Consider the equation $y”−y'−2y=0$. (a) Show that $y_1(t)=e^{−t}$ and $y_2(t)=e^{2t}$ form a fundamental set of solutions. (b) Let $y_3(t)=−2e^{2t}$, $y_4(t)=y_1(t)+2_{y2}(t)$, and $y_5(t)=2_{y1}(t)−2_{y3}(t)$. Are $y_3(t)$, $y_4(t)$, and $y_5(t)$ also solutions of the given differential equation? (c) Determine whether each of the following pairs forms a fundamental set of solutions: $[y_1(t),y_3(t)];[y_2(t),y_3(t)];[y_1(t),y_4(t)];[y_4(t),y_5(t)]$.

Solutions

VerifiedSolution A

Solution B

Answered 8 months ago

Step 1

1 of 4We were given

$y''-y'-2y=0 \tag{1}$

and $y_1(t)=e^{-t}$ and $y_2(t)=e^{2t}$.

Answered 10 months ago

Step 1

1 of 4In this problem we consider the ODE

$y''-y'-2y=0$

and we are asked to show that $y_1(t)=e^{-t}$ and $y_2(t)=e^{2t}$ form a fundamental set of solutions.

*What is a fundamental set of solutions?*

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