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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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Find the general solution $\large\frac{dy}{dx}$$=(1+x^2)(1+y^2)$

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1 Answer

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Toolbox:
  • $\int\large\frac{ dx}{1+x^2}$$ = \tan^{-1} x$
Step 1:
Given: $\large\frac{dy}{dx}$$ = (1 + x^2) (1 + y^2)$
Seperating the variables we get,
$\large\frac{dy}{1+y^2} $$= (1+x^2)$
Step 2:
Integrating on both sides, by using the information in the tool box,
$\tan^{-1}y$$ = x + x^3 + C$
This is the required general equation.
answered Aug 15, 2013 by sreemathi.v
 
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