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3 years ago

Does 4x+5y=0 represent a direct variation ?

Mathematics

2 answers:

omeli [17]3 years ago

7 0

4x+5y=0

subtract 4x from each side

5y = -4x

divide by 5

y = -4/5 x

y = kx where k = -4/5

this is a direction variation

trapecia [35]3 years ago

6 0

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 4x+5y=0\implies 5y=-4x\implies y=-\cfrac{4}{5}x\qquad \boxed{k=-\cfrac{4}{5}}\qquad \text{\Large\checkmark}$

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Differentiating with respect to $y$ yields

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Thus the solution to the ODE is

$\Psi(x,y)=x^7y+x^6y^{-1}=C$

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