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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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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)$

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  • 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.
answered Aug 16, 2013 by sreemathi.v

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