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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS3 Marks
Question
Solve the following differential equation:

y(1 - x2) $\frac{\text{dy}}{\text{dx}}$ = x(1 + y2).

✓

Answer

Writing y(1 - x2) $\frac{\text{dy}}{\text{dx}}$ = x(1 + y2) as $\int\frac{\text{ydy}}{\text{1 + y}^{2}}=\int\frac{\text{x}}{\text{1 - x}^{2}}\text{dx}$
$\Rightarrow$ log|1 + y2| = - log|1 - x2| + log C1
$\Rightarrow$ (1 + y2). (1 - x2) = C.

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