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Smitarani Swain posted an Question
May 05, 2022 • 12:59 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Thematics tial equation (6) ecot x/2 (a) en /2 (d) log cot log tan 51. the solution of (x + 1) =1-e is 763 sin nx equation (x+y-2) (x+ y) is the olution oft 2 d

THEMATICS TIAL EQUATION (6) ecot x/2 (a) en /2 (d) log cot log tan 51. The solution of (x + 1) =1-e is 763 sin nx equation (x+y-2) (x+ y) is The olution oft 2 dy dx (a) t)=log (-x+ 1) +C /y-)= log (r*y- 1) +C (a) r+1)e = x+ C (b) (x+ 1) (1 + e') =C (c) +1 =C (1+e) d) 2x=log (x+y+ 1) +C lution of the differential equation, cOS nx (d) =C 1-e) -2x= log *y- 1) +C 152. 1he differential equation =k(a - y) (b-y) w dx SOlved with the condition y(0) = 0, yields the result The dy-3+2y =e", y=3 and =3, when x = 0 is dx b(a - y)-a-b) kx (a) a (b - y) (a) y=2e te 2 - xe (b) y= 2er + e2 solution of the differential equation dx +22x- xe (d) =e - ex+ xex ab-y)_Sa-b)x (b) (C)y=e b(a - y) x quation The y= prt V4+p is l (y-Cx)-C=4 (6) (- Cx)2-4C2=0 cl y-Cx)+ C=0 (d) (y- Cx)? + 4C2 = 0 orthogonal trajectory to the family of circles (ba-x)-)k a(b - x) d) xy = kC 153. y= px - 2p find its singular solution (a) 8y= x (b) -4y-0 The = 2cx (c arbitrary) is describe by the differential (c) x=2y eguation, nl 2+y) y= 2xy (6) (-)y=2ay ( 2-xy' = y (d) -x)y= 21y (d) x2=y 154. Ify), y,) are solutions of y" +y' +(1 - x)y = sin x, then which of the following is also its solution? (a) y,)+ y) 6),)-y,) () 2y,)-V,) (d) y,)-2y,) ANSWERS -41C 2. (b) 4. (d) 7.(6) 3. (d) 13. (b) 5. (d) 6. (a) 8. (d) 9. (c) 10. (d) 14. (c) 15. (b) 17.(b) 18. (b) 19. (C) 20. (b) 16. (c) 26. (c) 36. (6) 12. (6) 28. (c) 30. () 27. () 37.(C) 29. (d) 39. (c) 22. (a) 23. (c) 24. () 25. (a) 32. (c) 33. (b) 34. (b) 35. (a) 38. (a) 40. (a) a) 47.(a) 49. (a) 50. (d) 48. (a) 58. (c) 42. (a) 43. (C) 44. (d) 45. (b) 46. (c) 60. (b) 70. (c) 59. (a) 57. (d) 67. (b) 77. (a) 53. (a) 54. (b) 55. (C) 56. (a) a) 52. (a) 68. (a) 69. (a) 64. (c) 65. (d) 66. (b) 62. (a) 63. (d) 78.(a) 79. (c) 80. (a) 75. (c) 76. (d) 72. (C) 73. (a) 74. (6) 87.(b) 88. (d) 89. (b) 90. (b) 85. (c) 86. (a) 84. (a) 94. (C) 82. (c) 83. (a) 97.(a) 98. (d) 99. (a) 100. (b) 95. (d) 96. (d) 110. (c) 92. (a) 93. (a) 107. (b) 108. (b) 109. (a) 105. (a) 106. () 120. (b) 104. (a) 118. (c) 119. (C) 117.(b) 127.(6) 103. (b) 102. (b) 112. (a) 115. (a) 116. (c) 130. (d) 128. (c) 129. (c) 114. (b) 124. (a) 134. (d) 113. (d) 126. (a) 140. (d) 138. (b) 139. (c) 149. (a) 125. (a) 122. (c) 123. (b) 136. (c) 137.(d) 150. (d) 135. (6) 148. (b) 147. (b) 132. (a) 133. (d) 146. (a) 145. () 142. (a) 143. (c) 144. (a) .PLEASE SOLVE ALL THE QUESTIONS

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  • Anonymous User best-answer

    153 (A) y=px-2p². (1) differential wrt p 0= x-4p p=x/4 from (1) y=x²/4-2x²/16 x²=8y

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