Page 161 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes
dy x y cosx

7. 

dx 1 sin x
dy y 2
8. For x > 0,   y x sin x given that y = 1 when x = 
dx x
~
3
2
9. 2xy = y 2x where y(1) = 2
dy
y
10. cosx  4 sin x  4 y sec x
dx
dy 2
y
11. tan y  tan x  cos cos x
dx

dy 3 3




12.  1 x (y x ) x (y x )
dx
2 dy 2 2 3
y
13. 2 cosy  sin y  (x 1)
dx x  1
y  dy  x

14. e   1  e
 dx 
dy y
15. dx  x  xy

Answers: Self Assessment

1. relationship 2. linear

3. multiply 4. Leibnitz’s linear equation

5. ye  Pdx   Qe  Pdx dx , c 6. solutions

7. linearly 8. consistent

9. Bernoulli’s equation 10. add

dy
y
11. decreases 12. f ' ( )  Pf   y  Q
dx
dy dz
y
13. constants 14. f ' ( ) . 
dx dx

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