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Differential Equations

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  1. 51.If y=y(x) is the solution curve of the differential equation (x^2-4)dy-(y^2-3y)dx=0,x>2,y(…
  2. 52.Let x=x(t) and y=y(t) be solutions of the differential equations (dx)/(dt)+ax=0 and (dy)/(…
  3. 53.Let x=x(y) be the solution of the differential equation 2(y+2) _e(y+2)dx+(x+4-2 _e(y+2))dy…
  4. 54.Let y=y_1(x) and y=y_2(x) be the solution curves of the differential equation [(d y)/(d x)…
  5. 55.Let y=y(x),y>0, be a solution curve of the differential equation (1+x^2)dy=y(x-y)dx.
  6. 56.Let y=y(x) be the solution of the differential equation (dy)/(dx)+5x(x^5+1)y=(x^5+1)^2x^7,…
  7. 57.Let y=y(x) be a solution curve of the differential equation.
  8. 58.Let f be a differentiable function such that x^2f(x)-x=4 _0^xtf(t)dt, f(1)=(2)/(3).
  9. 59.If the solution curve f(x,y)=0 of the differential equation (1+ _ex)(dx)/(dy)-x _ex=e^y,x>…
  10. 60.Let y=y(x) be the solution of the differential equation (3y^2-5x^2)ydx+2x(x^2-y^2)dy=0 suc…
  11. 61.The solution of the differential equation (dy)/(dx)=-(x^2+3y^23x^2+y^2),y(1)=0 is :
  12. 62.The differential equation satisfied by the system of parabolas y2 = 4a(x + a) is :
  13. 63.The differential equation of the family of curves, x2 = 4b(y + b), b [ ] R, is :
  14. 64.Let y=y(x) be the solution of the differential equation (x^2-xx^2-1)dy+(y(x-x^2-1)-x)dx=0,…
  15. 65.Let y=y(x) be the solution of the differential equation ( x)^1/2dy=( ^3x-( x)^3/2y)dx,0
  16. 66.Let y=y(x) be the solution of the differential equation x ((y)/(x))dy=(y ((y)/(x))-x)dx,y(…
  17. 67.Let f be a twice differentiable function such that f(x)= _x^0 (t-x)dt- _x^0f(t) tdt,x (-( …
  18. 68.If the solution curve y=f(x) of the differential equation (x^2-4)y^'-2xy+2x(4-x^2)^2=0,x>2…
  19. 69.Let f be a twice differentiable non-negative function such that (f(x))^2=25+_0^x((f(t))^2+…
  20. 70.Let y=y(x) be the solution of the differential equation (dy)/(dx)+2y ^2x=2 ^2x+3 x ^2x suc…
  21. 71.If y=y(x) is the solution of the differential equation, √4-x^2(dy)/(dx)=(( ^-1((x)/(2)))^2…
  22. 72.Let y=y(x) be the solution of the differential equation 2 x(dy)/(dx)= 2x-4y x,x (0,( )/(2)…
  23. 73.Let f be a differentiable function such that 2(x+2)^2f(x)-3(x+2)^2=10 _x^0(t+2)f(t)dt,x 0.
  24. 74.Let y=f(x) be the solution of the differential equation (dy)/(dx)+xyx^2-1=x^6+4x√1-x^2,-1<…
  25. 75.For a differentiable function f:R R, suppose f^'(x)=3f(x)+ , where R,f(0)=1 and x -limf(x)…
  26. 76.Let |x|=|y|e^xy- , , N be the solution of the differential equation xdy-ydx+xy(xdy+ydx)=0,…
  27. 77.If the solution y(x) of the given differential equation (e^y+1) xdx+e^y xdy=0 passes throu…
  28. 78.Let y=y(x) be the solution of the differential equation (dy)/(dx)+2x(1+x^2)^2y=xe^1(1+x^2)…
  29. 79.Let y=y(x) be the solution of the differential equation (x+y+2)^2 d x=d y, y(0)=-2.
  30. 80.If (dx)/(dy)=1+x-y^2y,x(1)=1, then 5x(2) is equal to __________.
  31. 81.If x=x(t) is the solution of the differential equation (t+1)dx=(2x+(t+1)^4)dt,x(0)=2, then…
  32. 82.Let y=y(x) be the solution of the differential equation ^2xdx+(e^2y ^2x+ x)dy=0,0<x<( )/(2…
  33. 83.Let Y=Y(X) be a curve lying in the first quadrant such that the area enclosed by the line …
  34. 84.Let y=y(x) be the solution of the differential equation (1-x^2)dy=[xy+(x^3+2)√3(1-x^2)]dx,…
  35. 85.If the solution curve y=y(x) of the differential equation (1+y^2)(1+ _ex)dx+xdy=0,x>0 pass…
  36. 86.If the solution curve, of the differential equation (dy)/(dx)=(x+y-2)/(x-y) passing throug…
  37. 87.If the solution of the differential equation (2x+3y-2)dx+(4x+6y-7)dy=0,y(0)=3, is x+ y+3 _…
  38. 88.If y=y(x) is the solution of the differential equation (dy)/(dx)+4x(x^2-1)y=x+2(x^2-1)^(5)…
  39. 89.Let the tangent at any point P on a curve passing through the points (1, 1) and [((1)/(10)…
  40. 90.Let the solution curve x=x(y),0<y<( )/(2), of the differential equation ( _e( y))^2 ydx-(1…
  41. 91.If the solution curve of the differential equation (y-2 _ex)dx+(x _ex^2)dy=0,x>1 passes th…
  42. 92.Let y=y(x) be a solution of the differential equation [(x x) d y+(x y x+y x-1) d x=0,0 < x…
  43. 93.The area enclosed by the closed curve C given by the differential equation dydx+x+ay-2=0, …
  44. 94.Let y=f(x) be a twice differentiable non-negative function such that [y^2 = 25 + _0^x ((f(…
  45. 95.Let f be a twice differentiable function such that [f(x) = _0^x (t-x),dt - _0^x f(t) t,dt,…
  46. 96.Let y=y(x) be the solution of the differential equation [( x)^1/2,dy = (^3 x - ( x)^3/2y)d…
  47. 97.Let y=y(x) be the solution of the differential equation [(x^2-xx^2-1),dy + (y(x-x^2-1)-x),…
  48. 98.Let y=y(x) be the solution of the differential equation [(1+x^2),dy + (y-^-1x),dx=0, y(0)=…
  49. 99.Let y=y(x) be the solution of the differential equation [ x(dy)/(dx) - 2y = 2+3 x, x(-()/(…
  50. 100.Let y=y(x) be the solution of the differential equation [x^4,dy + (4x^3y+2 x),dx=0, x>0, y…