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Differential Equations

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  1. 351.The solution of the differential equation [dy dx, + ,y 2, x = x 2y,,,] where 0 [ ] x < [ 2…
  2. 352.If f(x) is a differentiable function in the interval (0, [ ]) such that f (1) = 1 and [ _t…
  3. 353.If [( 2 + x )dy dx + ( y + 1 ) x = 0] and y(0) = 1, then [y( 2 )] is equal to :
  4. 354.The curve satisfying the differential equation, ydx -(x + 3y2)dy = 0 and passing through t…
  5. 355.If 2x = y[^1 5] + y[^ - 1 5] and (x2 - 1) [d^2y dx^2] + [ ]x [dy dx] + ky = 0, then [ ] + …
  6. 356.Let y = y(x) be the solution of the differential equation [ xdy dx + y x = 4x], [x ( 0, )]…
  7. 357.The curve satifying the differeial equation, (x2 - y2) dx + 2xydy = 0 and passing through …
  8. 358.The differential equation representing the family of ellipse having foci eith on the x-axi…
  9. 359.Let y = y(x) be the solution of the differential equation, [dy dx + y x = 2x + x^2 x], [x …
  10. 360.If y = y(x) is the solution of the differential equation [dy dx = ( x - y ) ^2x], [x ( - 2…
  11. 361.Let f be a differentiable function such that f '(x) = 7 - [3 4f( x ) x,] (x > 0) and f(1) …
  12. 362.The curve amongst the family of curves represented by the differential equation, (x2 -- y2…
  13. 363.If [dy dx + 3 ^2xy = 1 ^2x,,,x ( - 3, 3 )] and [y( 4 ) = 4 3,] then [y( - 4 )] equals -
  14. 364.The solution of the differential equation, [dy dx] = (x -- y)2, when y(1) = 1, is :
  15. 365.If y(x) is the solution of the differential equation [dy dx + ( 2x + 1 x )y = e^ - 2x,,,x …
  16. 366.The general solution of the differential equation (y2 -- x3)dx -- xydy = 0 (x [ ] 0) is : …
  17. 367.Consider the differential equation, [y^2dx + ( x - 1 y )dy = 0], If value of y is 1 when x…
  18. 368.If a curve passes through the point (1, --2) and has slope of the tangent at any point (x,…
  19. 369.Let y = y(x) be the solution of the differential equation, x[dy dx] + y = x loge x, (x > 1…
  20. 370.Let y = y(x) be the solution of the differential equation, [(x^2 + 1)^2dy dx + 2x(x^2 + 1)…
  21. 371.If [ xdy dx - y x = 6x], (0 < x < [ 2]) and [y( 3 )] = 0 then [y( 6 )] is equal to :-
  22. 372.The solution of the differential equation [xdy dx + 2y] = x2 (x [ ] 0) with y(1) = 1, is :
  23. 373.Let f : [0,1] [ ] R be such that f(xy) = f(x).f(y), for all x, y [ ] [0, 1], and f(0) [ ] …
  24. 374.If y = y(x) is the solution of the differential equation, x[dy dx] + 2y = x2, satisfying y…
  25. 375.If a curve y = f(x), passing through the point (1, 2), is the solution of the differential…
  26. 376.Let y = y(x) be the solution of the differential equation, [2 + x y + 1.dy dx = - x], y > …
  27. 377.If x3dy + xy dx = x2dy + 2y dx; y(2) = e and x > 1, then y(4) is equal to :
  28. 378.The solution curve of the differential equation, (1 + e-x)(1 + y2) (dy dx] = y2, which pas…
  29. 379.The solution of the differential equation [dy dx - y + 3x _e( y + 3x ) + 3 = 0] is: (where…
  30. 380.Let y = y(x) be the solution of the differential equation, xy'- y = x2(xcosx + sinx), x > …
  31. 381.Let y = y(x) be the solution of the differential equation cosx[dy dx] + 2ysinx = sin2x, x …
  32. 382.If y = y(x) is the solution of the differential equation [5 + e^x 2 + y.dy dx + e^x = 0] s…
  33. 383.If [y = ( 2 x - 1 ) cosec,x] is the solution of the differential equation, [dy dx + p( x )…
  34. 384.The general solution of the differential equation [ 1 + x^2 + y^2 + x^2y^2 ] + xy[dy dx] =…
  35. 385.Let y = y(x) be the solution curve of the differential equation, [( y^2 - x )dy dx = 1], s…
  36. 386.If y = y(x) is the solution of the differential equation, [e^y( dy dx - 1 ) = e^x] such th…
  37. 387.Let y = y(x) be a solution of the differential equation, [ 1 - x^2 dy dx + 1 - y^2 = 0], |…
  38. 388.If y = y(x) is the solution of the differential equation [dy dx] + (tan x) y = sin x, [0 x…
  39. 389.Let C1 be the curve obtained by the solution of differential equation [2xydy dx = y^2 - x^…
  40. 390.If y = y(x) is the solution of the differential equation, [dy dx + 2y x = x,y( 3 ) = 0], t…
  41. 391.If the curve y = y(x) is the solution of the differential equation [2(x^2 + x^5/4)dy - y(x…
  42. 392.Let y = y(x) be the solution of the differential equation [ x(3 x + x + 3)dy = (1 + y x(3 …
  43. 393.Which of the following is true for y(x) that satisfies the differential equation [dy dx] =…
  44. 394.Let y = y(x) be the solution of the differential equation [dy dx = (y + 1)( (y + 1)e^x^2/2…
  45. 395.If y = y(x) is the solution curve of the differential equation [x^2dy + ( y - 1 x )dx = 0]…
  46. 396.Let y = y(x) be the solution of the differential equation [x ( y x )dy = ( y ( y x ) - x )…
  47. 397.Let y = y(x) be the solution of the differential equation [e^x 1 - y^2 dx + ( y x )dy = 0]…
  48. 398.Let y = y(x) be the solution of the differential equation [ ec^2xdy + 2dx = (1 + y 2x) ec^…
  49. 399.If a curve y = f(x) passes through the point (1, 2) and satisfies [x dy dx + y = bx^4], th…
  50. 400.The population P = P(t) at time 't' of a certain species follows the differential equation…