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# Form the differential equuations by eliminating arbitary constants given in brackets against each. $y^{2}=4ax [a]$

Toolbox:
• If we have an equation $f(x,y,c_1,c_2,....c_n)=u$ Containing n arbitrary constant $c_1,c_2...c_n$, then by differentiating n times, we get $(n+1)$ equations in total. If we eliminate the arbitrary constants $c_1,c_2....c_n,$ we get a D.E of order n
Step 1:
$y^2= 4ax$ -----(i)
$2y \large\frac{dy}{dx}$$= 4a-----(ii) Step 2: Substituting from (ii) in (i) y^2= 2y \large\frac{dy}{dx}$$.x$