Question
Solve the following differential equations:
$(\text{y}^2+1)\text{dx}-(\text{x}^2+1)\text{dy}=0$
$(\text{y}^2+1)\text{dx}-(\text{x}^2+1)\text{dy}=0$
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Answer
$(\text{y}^2+1)\text{dx}-(\text{x}^2+1)\text{dy}=0$
$(\text{y}^2+1)\text{dx}=(\text{x}^2+1)\text{dy}$
$\int\frac{\text{dy}}{\text{y}^2+1}=\int\frac{\text{dx}}{\text{x}^2+1}$
$\tan^{-1}\text{y}=\tan^{-1}\text{x + C}$
$(\text{y}^2+1)\text{dx}=(\text{x}^2+1)\text{dy}$
$\int\frac{\text{dy}}{\text{y}^2+1}=\int\frac{\text{dx}}{\text{x}^2+1}$
$\tan^{-1}\text{y}=\tan^{-1}\text{x + C}$
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