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Calculus Level 4

S o l u t i o n o f t h e d i f f e r e n t i a l e q u a t i o n x 2 d y d x . c o s ( 1 x ) − y s i n ( 1 x ) = − 1 w h e r e y → − 1 a s x → ∞ i s . Solution\quad of\quad the\quad differential\quad equation\quad { x }^{ 2 }\frac { dy }{ dx } .cos(\frac { 1 }{ x } )-ysin(\frac { 1 }{ x } )=-1\\ where\quad y\rightarrow -1\quad as\quad x\rightarrow \infty \quad is.

y = s i n 1 x + c o s 1 x y=sin\frac { 1 }{ x } +cos\frac { 1 }{ x } y = x + 1 x c o s ( 1 x ) y=\frac { x+1 }{ xcos(\frac { 1 }{ x } ) } y = x + 1 x s i n ( 1 x ) y=\frac { x+1 }{ xsin(\frac { 1 }{ x } ) } y = s i n 1 x − c o s 1 x y=sin\frac { 1 }{ x } -cos\frac { 1 }{ x }

Mehul Chaturvedi by Mehul Chaturvedi , 22, India

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1 solution

Siddharth Yadav
Mar 25, 2017

Rearrange to get a first order differential equation With integrating factor as 1/cos(1/x).

0 Helpful 1 Interesting 0 Brilliant 0 Confused

The options ought to be better . I just evaluated the limits for x-> infinity for the given equations and the fourth one matched .

Arghyadeep Chatterjee - 3 years, 1 month ago

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