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# Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=Ax\qquad:\;xy'\;=\;y\;(x\neq0)$

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## 1 Answer

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Toolbox:
• Differentiation of $AX = A$
Given $y = Ax$
Differentiating on both sides we get
$y' = A$
Step 2:
Multiply on both sides by $x$ we get
$xy' = AX$
But $AX = y$
Hence $xy' = y$
The answer is a solution to the given solution.
answered Aug 19, 2013

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