Wronskian The Wronskian of two differentiable functions and denoted by is defined as the
Chapter 16, Problem 66(choose chapter or problem)
Wronskian The Wronskian of two differentiable functions f and g, denoted by W(f, g), is defined as the function given by the determinant
\(W(f, g)=\left|\begin{array}{ll} f & g \\ f^{\prime} & g^{\prime} \end{array}\right| \)
The functions f and g are linearly independent when there exists at least one value of x for which \(W(f, g) \neq 0\). In Exercises 65-68, use the Wronskian to verify the linear independence of the two functions.
\(y_{1}=e^{a x}\)
\(y_{2}=x e^{a x}\)
Text Transcription:
W(f,g)=|f g f’ g’|
W(f,g) neq 0
y_1=e^ax
y_2=x e^ax
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