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Differential Equations

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  1. 401.If a curve passes through the origin and the slope of the tangent to it at any point (x, y…
  2. 402.Let y = y(x) be the solution of the differential equation xdy = (y + x3 cosx)dx with y([])…
  3. 403.Let y = y(x) be the solution of the differential equation [dy dx = 1 + xe^y - x, - 2 < x <…
  4. 404.Let y(x) be the solution of the differential equation 2x2 dy + (ey - 2x)dx = 0, x > 0.
  5. 405.Let y = y(x) be a solution curve of the differential equation [(y + 1) ^2x,dx + x,dy + y,d…
  6. 406.The rate of growth of bacteria in a culture is proportional to the number of bacteria pres…
  7. 407.A differential equation representing the family of parabolas with axis parallel to y-axis …
  8. 408.If the solution curve of the differential equation (2x - 10y3)dy + ydx = 0, passes through…
  9. 409.Let y = y(x) be the solution of the differential equation [dy dx = 2(y + 2 x - 5)x - 2 x] …
  10. 410.Let us consider a curve, y = f(x) passing through the point (-2, 2) and the slope of the t…
  11. 411.Let y = y(x) be the solution of the differential equation (x - x3)dy = (y + yx2 - 3x4)dx, …
  12. 412.Let y = y(x) be solution of the differential equation [ _( dy dx ) = 3x + 4y], with y(0) =…
  13. 413.If [dy dx = 2^xy + 2^y.2^x 2^x + 2^x + y _e2], y(0) = 0, then for y = 1, the value of x li…
  14. 414.If [ydy dx = x[ y^2 x^2 + ( y^2 x^2 ) '( y^2 x^2 ) ]], x > 0, [] > 0, and y(1) = -1, then …
  15. 415.If [dy dx = 2^x + y - 2^x 2^y], y(0) = 1, then y(1) is equal to :
  16. 416.If x = x(y) is the solution of the differential equation [ydx dy = 2x + y^3(y + 1)e^y,,x(1…
  17. 417.Let a smooth curve y=f(x) be such that the slope of the tangent at any point (x, y) on it …
  18. 418.The slope of the tangent to a curve C: y=y(x) at any point (x, y) on it is [2 e^2 x-6 e^-x…
  19. 419.The general solution of the differential equation [(x-y^2) d x+y(5 x+y^2) d y=0] is :
  20. 420.If y = y(x) is the solution of the differential equation [2x^2dy dx - 2xy + 3y^2 = 0] such…
  21. 421.Let y = y(x) be the solution of the differential equation (x + 1)y' - y = e^3x(x + 1)^2, w…
  22. 422.If the solution curve y = y(x) of the differential equation y^2dx + (x^2 - xy + y^2)dy = 0…
  23. 423.Let the solution curve y=f(x) of the differential equation [ (d y)/(d x)+x yx^2-1=x^4+2 x√…
  24. 424.If y = y(x) is the solution of the differential equation [xdy dx + 2y = x,e^x], y(1) = 0 t…
  25. 425.If the solution of the differential equation [dy dx + e^x( x^2 - 2 )y = ( x^2 - 2x )( x^2 …
  26. 426.Let y=y_1(x) and y=y_2(x) be two distinct solutions of the differential equation [(d y)/(d…
  27. 427.If the solution curve of the differential equation [(( ^ - 1y) - x)dy = (1 + y^2)dx] passe…
  28. 428.Let [dy dx = ax - by + a bx + cy + a], where a, b, c are constants, represent a circle pas…
  29. 429.If [dy dx + 2^x - y(2^y - 1) 2^x - 1 = 0], x, y > 0, y(1) = 1, then y(2) is equal to :
  30. 430.Let y=y(x) be the solution curve of the differential equation [ (d y)/(d x)+1x^2-1 y=((x-1…
  31. 431.The differential equation of the family of circles passing through the points (0,2) and (0…
  32. 432.Let the solution curve of the differential equation [x ~d y=(x^2+y^2+y) d x, x>0], interse…
  33. 433.If [y=y(x), x (0, / 2)] be the solution curve of the differential equation [( ^2 2 x) (d y…
  34. 434.Let x = x(y) be the solution of the differential equation [2y,e^x/y^2dx + ( y^2 - 4xe^x/y^…
  35. 435.Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 [ x( x - y)].
  36. 436.Let the solution curve y = y(x) of the differential equation [[ x x^2 - y^2 + e^y x ]xdy d…
  37. 437.Let y = y(x) be the solution of the differential equation [x(1 - x^2)dy dx + (3x^2y - y - …
  38. 438.If the solution curve of the differential equation [(d y)/(d x)=(x+y-2)/(x-y)] passes thro…
  39. 439.Let y=y(x) be the solution curve of the differential equation [ (d y)/(d x)+(2 x^2+11 x+13…
  40. 440.Let the solution curve y=y(x) of the differential equation [(1+e^2 x)(d y~d x+y)=1] pass t…
  41. 441.If y = y(x) is the solution of the differential equation [( 1 + e^2x )dy dx + 2( 1 + y^2 )…
  42. 442.Let the solution curve of the differential equation [xdy dx - y = y^2 + 16x^2 ], y(1) = 3 …
  43. 443.Let [dy dx = ax - by + a bx + cy + a,,a,b,c R], represents a circle with center ([], []).
  44. 444.Let y=y(x) be the solution of the differential equation [(d y)/(d x)+5x(x^5+1) y=(x^5+1)^2…
  45. 445.Let y=y(x) be a solution curve of the differential equation.
  46. 446.Let y=y(x), y > 0, be a solution curve of the differential equation [(1+x^2) d y=y(x-y) d …
  47. 447.Let y=y_1(x) and y=y_2(x) be the solution curves of the differential equation [(d y)/(d x)…
  48. 448.Let x=x(y) be the solution of the differential equation 2(y+2) _e(y+2) d x+(x+4-2 _e(y+2))…
  49. 449.Let [ x= (x^ y^)] be the solution of the differential equation [2 x^2 y ~d y-(1-x y^2) d x…
  50. 450.If y=y(x) is the solution curve of the differential equation [(d y)/(d x)+y x=x x, 0 x ()/…