Question
Download Solution PDFThe solution of the differential equation \(y\sqrt {1 - {x^2}} dy + x\sqrt {1 - {y^2}} dx = 0\) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven differential equation is,
\(y\sqrt {1 - {x^2}} dy + x\sqrt {1 - {y^2}} dx = 0\)
\(\Rightarrow \frac{y}{{\sqrt {1 - {y^2}} }}dy = \frac{{ - x}}{{\sqrt {1 - {x^2}} }}dx\)
By integrating both sides,
\(\smallint \frac{y}{{\sqrt {1 - {y^2}} }}dy = - \smallint \frac{x}{{\sqrt {1 - {x^2}} }}dx + {C_1}\)
(1 – y2)1/2 = - (1 – x2)1/2 + C
\(\Rightarrow \sqrt {\left( {1 - {y^2}} \right)} + \sqrt {\left( {1 - x} \right)} + C = 0\)Last updated on Jun 23, 2025
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