Clairaut's Equation

$y(x)=x\backslash frac\{dy\}\{dx\}+f\backslash left(\backslash frac\{dy\}\{dx\}\backslash right).$

$\backslash frac\{dy\}\{dx\}=\backslash frac\{dy\}\{dx\}+x\backslash frac\{d^2\; y\}\{dx^2\}+f\text{'}\backslash left(\backslash frac\{dy\}\{dx\}\backslash right)\backslash frac\{d^2\; y\}\{dx^2\},$

$0=\backslash left(x+f\text{'}\backslash left(\backslash frac\{dy\}\{dx\}\backslash right)\backslash right)\backslash frac\{d^2\; y\}\{dx^2\}.$

$0=\backslash frac\{d^2\; y\}\{dx^2\}$

$0=x+f\text{'}\backslash left(\backslash frac\{dy\}\{dx\}\backslash right).$

$y(x)=Cx+f(C),\backslash ,$

$0=x+f\text{'}\backslash left(\backslash frac\{dy\}\{dx\}\backslash right),$

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