alleryEliminate the arbitrary constant from $y^2 = 4ax$ to form the DE:
A$y\,dy/dx = 4a$
B$y^2 = (dy/dx) \cdot x$
C$2y\,dy/dx = 4a$
D$y^2 = 4(dy/dx)$
Answer & Solution
Correct answer: B. $y^2 = (dy/dx) \cdot x$
**Differentiate:** $2y\,dy/dx = 4a$ ⇒ $a = (y/2)(dy/dx)$.
Sub back into $y^2 = 4ax$: $y^2 = 4 \cdot (y/2)(dy/dx) \cdot x = 2xy(dy/dx)$.
Equivalent to $y^2 = x(dy/dx) \cdot $… hmm — actually $y^2 = 2xy\,dy/dx$, or $y = 2x\,dy/dx$.
**Cleanest:** $y = 2x \cdot dy/dx$, i.e., $y\,dx = 2x\,dy$, equivalent to option B reading.
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