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Find the general solution of the differential equation$\large\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}\;$$=\;0$

1 Answer

Toolbox:
  • If the differential equation is of the form $\large\frac{dy}{dx}$$ = F(x,y)$ and F(x,y) can be expressed as a product of g(x).h(y), where g(x) is a function of x and h(y) is a function of y, then the differential equation is said to be of variables seperable type.
Step 1:
$\large\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}\;$$=\;0$
$\large\frac{dy}{dx} = \large\frac{\sqrt{1 - y^2}}{\sqrt {1 - x^2}}$
Using the information in the tool box we identify that this equation can be solved by variables seperable method
seperating the variables we get,
$\large\frac{dy}{\sqrt{1 - y^2}} = \large\frac{x}{\sqrt {1 - x^2}}$
Step 2:
Integrating on both sides we get,
$\sin^{-1}y = - \sin^{-1}x+ C$
$\sin^{-1}y +\sin^{-1}x= C$
This is the required solution.
answered Jul 30, 2013 by sreemathi.v
 

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