Example 5 - Find general solution: dy/dx = 1+y2 / 1+x2 - Examples - Examples

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Example 5 Find the general solution of the differential equation 𝑑𝑦/𝑑π‘₯=(1 + 𝑦^2)/(1 + π‘₯^2 ) 𝑑𝑦/𝑑π‘₯=(1 + 𝑦^2)/(1 + π‘₯^2 ) π’…π’š/(𝟏 + π’šπŸ)=𝒅𝒙/(𝟏 + 𝒙^𝟐 ) Integrating both sides ∫1▒𝑑𝑦/(1 + 𝑦^2 ) = ∫1▒𝑑𝑦/(1 + π‘₯^2 ) tanβˆ’1 y = tanβˆ’1 x + c tanβˆ’1 y = tanβˆ’1 x + c is the general solution of the given equation (∫1β–’1/(1 + π‘₯^2 ) dx = tanβˆ’1 x + c)

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