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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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Find a particular solution satisfying the given condition $\cos\bigg(\large\frac{dy}{dx}\bigg)$$=a\;(a\;\in\;R);y=2\;when\;x=0$

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  • If $\cos x = a$, then $x =\cos^{-1}a$
Step 1:
Given $\cos(\large\frac{dy}{dx}) =$$ a$
Using information in the tool box:
$\large\frac{dy}{dx} $$=\cos^{-1}a.$
Separating the variables we get,
$dy = \cos^{-1}a$
Step 2:
Integrating on both sides we get,
$\int dy = \int\cos^{-1}a.dx$
$y = \cos^{-1}a.x + C$
$y = 1$ and $x =0$
$1 = 0.\cos^{-1}a + C$
$C = 1$
Step 3:
Substituting the value of $C$ we get
$y - x\cos^{-1}a = 1$
This is the required equation.
answered Aug 14, 2013 by sreemathi.v

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