# Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=\sqrt{a^2-x^2}\;x\in\;(-a,a):\;x+y\;\large\frac{dy}{dx}$$=0(y\neq0) ## 1 Answer Toolbox: • Differentiation \sqrt{ a^2 - x^2} is \large\frac{-x}{\sqrt{ a^2 - x^2 }} Step 1: Given : y = \sqrt{ a^2 - x^2} Differentation on both sides we get, \large\frac{dy}{dx} = \frac{1}{2}$$ (a^2 - x^2) ^{-1/2} . -2x$
on simplifying we get
$\large\frac{-x}{\sqrt{ a^2 - x^2}}$
Step 2:
Substituting for $\large\frac{dy}{dx}$ in the given solution we get,
$x + y. \large\frac{-x}{\sqrt{a^2 - x^2}}$$= 0 Now substituting for y we get x + \sqrt{ a^2 - x^2} . \large\frac{-x}{\sqrt{a^2 - x^2}}$$= 0$
Step 3:
on simplifying we get
$x - x = 0$
Hence LHS = RHS.
Hence the given solution is verified.