The functions 1, x, and x^2 are solutions to the equation y'''(x) = 0. Determine whether they are linearly independent or dependent.

Question

The functions [latex]1, x[/latex], and [latex]x^{2}[/latex] are solutions to the equation [latex]y^{\prime \prime \prime}(x)=0 .[/latex] Determine whether they are linearly independent or dependent.

Accepted Answer

[latex]W\left(y_{1}, y_{2}, y_{3} ight)=\left|\begin{array}{lll}1 & x & x^{2} \0 & 1 & 2 x \0 & 0 & 2\end{array} ight|=2 eq 0[/latex]

so the functions are linearly independent.

Question 11.15.1: The functions 1, x, and x^2 are solutions to the equation y'...

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