CH 9 Differential Equations Multiple Choice Questions (With Answers) [PDF]

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MULTIPLE CHOICE QUESTIONS CHAPTER – 9 DIFFERENTIAL EQUATIONS 3



 d 2 y   dy   dy  Q1. The degree of the differential equation  2      sin    1  0 is:  dx   dx   dx 



(a) 3



2



(b) 2



(c) 1



(d) not defined



d2y dy Q2. The order of the differential equation 2 x  3  y  0 is: 2 dx dx 2



(a) 2



(b) 1



(c) 0







(d) not defined







Q3. The solution of the differential equation e x 1 y dy   y 1 e x dx is:











(a) e y  c e x 1  y 1







Q4. The solution of the differential equation



(a) e1 y  x 



x2 c 2











(d) none of these



dy 1  x  y  xy is: dx



(b) log 1  y  x 



Q5. The solution of the differential equation







(c) y  e x 1  y 1



(b) e y  c e x  y 1



x2 c 2



(c) e y  x 



x2 c 2



(d) none of these



dy 1 y 2   0 is: dx 1 x2



(a) y  sin 1 y  sin 1 x  c (b) sin 1 y  sin 1 x  c



(c) sin 1 y  sin 1 x  c



(d) none of these



Q6. The solution of the differential equation x 1 y 2 dx  y 1 x 2 dy  0 is: (a) sin 1 x  sin 1 y  c



Q7. The solution of the differential equation (a) x 2  y 2  cx



(d) none of these



dy y 2  x 2 is:  dx 2 xy



(b) x 2  y 2  cy



Q8. The solution of the differential equation (a) y  sin x  c cos x



(c) tan 1 x  tan 1 y  c



(b) 1 x 2  1 y 2  c



(c) x 2  y 2  cx



(d) none of these



dy  y tan x  sec x is: dx



(b) y  sin x  c cos x



(c)  y  sin x  sin x  c



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(d) none of these



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Q9. The integrating factor of the differential equation  x log x  (a) log  log x 



(b) e x



dy  y  2log x is: dx



(c) log x



Q10. The solution of the differential equation



(d) x



dy y   sin x is: dx x



(a) x  y  cos x   sin x  c (b) x  y  cos x   sin x  c (c) x  y  cos x   cos x  c Q11. The solution of the differential equation 2 x (a) circles



(a) sin



dy  y  3 represents: dx



(b) straight lines



(c) ellipses



Q12. The solution of the differential equation x



x  xc y



(b) sin



(d) parabolas



dy y  y  x tan is: dx x



y  cx x



(c) sin



Q13. The solution of the differential equation x 2  y 2 (a) x2  y 2 12 x  c



(d) none of these



(b) x2  y 2  3x  c



x  cy y



(d) sin



y  cy x



dy  4 is: dx (d) x3  y3 12 x  c



`(c) x3  y3  3x  c



Q14. The solution of the differential equation x dx  y dy  x 2 y dy  y 2 x dx is:







(a) x 2 1 c 1 y 2











(b) x 2 1  c 1 y 2















(c) x3 1 c 1 y 3



 y  dy dx



Q15. The solution of the differential equation x 2  1 (a) y  2  x 2



(b) y 



1 x 1 x







(d) x3 1  c 1 y 3







 1  0 is:



(c) y  x  x 1



Q16. The solution of the differential equation



x (a) tan 1    log y  c  y



2







(d) y 



1 x 1 x



dy x 2  xy  y 2  is: dx x2



x  y (b) tan 1    log x  c (c) tan 1    log x  c x  y



(d) none of these



ANSWERS 1. d d



2. a 3. a 16. d



4. b



5. c



6. b



7. c



8. b



9. c



10. a



11. d



12. b



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13. d



14. a 15. Page 2