431,818 views
12 votes
12 votes
Find the general solution of the differential equation


(dy)/(dx) = (1 + {x}^(2) )(1 + {y}^(2) )


User Nate Hekman
by
2.2k points

1 Answer

7 votes
7 votes


{ \pink{ \tt{ { \tan }^( - 1) y - \frac{ {x}^(3) }{3} = c }}}

Explanation:

This can be written as,


{ \green{ \tt \frac{dy}{1 + {y}^(2)}}} = { \green{ \tt{(1 + {x}^(2))dx}}}

Integeare on both sides, then


{ \blue{ \tt{ ∫  \frac{1}{1 + {y}^(2)}}}}{ \blue{ \tt{dy}}} = { \blue{ \tt{  ∫ (1 + {x}^(2) )dx}}}


{ \blue{ \tt{ { \tan }^( - 1) y = \frac{ {x}^(3) }{3} + c}}}


{ \huge{ \green{ \blue{ \tt{ { \tan }^( - 1) y - \frac{ {x}^(3) }{3} = c}}}}}

User Mohsen
by
2.9k points