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Differential Equations

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  1. 301.If the general solution of y'=yx+(xy) is y|cx|=x (c arbitrary), then (2) is:
  2. 302.If dydx+y x=2x, y(0)=1, then y() equals:
  3. 303.The general solution of 2xdydx- x-y=0 is:
  4. 304.Statement-1: The slope of a tangent to y^2=4ax (axis of x) is inversely proportional to th…
  5. 305.A firm manufacturing 2000 items estimates dPdx=100-12 x.
  6. 306.If a curve passes through (2,72) with slope 1-1x^2, the ordinate at abscissa -2 is:
  7. 307.Consider dydx=y^32(xy^2-x^2).
  8. 308.The equation of the curve through the origin satisfying (1+x^2)dydx+2xy=4x^2 is:
  9. 309.Statement-1: The degrees of dydx+y^2=x and d^2ydx^2+y= x are equal.
  10. 310.The population p(t) satisfies dp(t)dt=0.5p(t)-450, p(0)=850.
  11. 311.Let y(x) solve (2+ x)(1+y)dydx= x.
  12. 312.The integrating factor of (x^2-1)dydx+2xy=x is:
  13. 313.The general solution of dydx+2xy=x^2 is:
  14. 314.The curve through (2,3) such that the segment of any tangent between the axes is bisected …
  15. 315.V(t) depreciates per dVdt=-k(T-t), k>0.
  16. 316.If dydx=y+3>0, y(0)=2, then y(2) is:
  17. 317.Consider y^2,dx+(x-1y)dy=0.
  18. 318.Solution of x,dy=y( x-y),dx, 0<x</2, is:
  19. 319.The differential equation representing y=c_1e^c_2x, c_1,c_2 arbitrary, is:
  20. 320.The differential equation of circles with fixed radius 5, centre on y=2, is:
  21. 321.The solution of dydx=x+yx, y(1)=1, is:
  22. 322.The differential equation of all circles through the origin with centres on the x-axis is:
  23. 323.The normal to y=y(x) at P(x,y) meets the x-axis at G.
  24. 324.The differential equation whose solution is Ax^2+By^2=1 (A,B arbitrary) has:
  25. 325.The differential equation representing y^2=2c(x+ c), c>0, has order and degree:
  26. 326.If xdydx=y( y- x+1), the solution is:
  27. 327.The differential equation for the family of circles x^2+y^2-2ay=0 (a arbitrary) is:
  28. 328.Solution of y,dx+(x+x^2y),dy=0 is:
  29. 329.The degree and order of the differential equation of the family of all parabolas whose axi…
  30. 330.The solution of (1+y^2)+(x-e^^-1y)dydx=0 is:
  31. 331.The order and degree of [1+3(dydx)^2]^2/3=4d^3ydx^3 are:
  32. 332.The solution of d^2ydx^2=e^-2x is:
  33. 333.The order and degree of the differential equation [,( 1 + 3dy dx )^2/3 = 4d^3y dx^3] are
  34. 334.The solution of the differential equation [( 1 + y^2 ) + ( x - e^ ^ - 1y )dy dx = 0,] is :
  35. 335.Solution of the differential equation [ydx + ( x + x^2y )dy = 0] is
  36. 336.The differential equation for the family of circle x^2 + y^2 - 2ay = 0, where a is an arbi…
  37. 337.The differential equation representing the family of curves [y^2 = 2c( x + c ),] where c>0…
  38. 338.If [xdy dx = y( y - x + 1 ),] then the solution of the equation is :
  39. 339.The differential equation whose solution is Ax^2 + By^2 = 1 where A and B are arbitrary co…
  40. 340.The differential equation of all circles passing through the origin and having their centr…
  41. 341.The solution of the differential equation [dy dx = x + y x] satisfying the condition y(1)=…
  42. 342.The differential equation which represents the family of curves y = c_1e^c_2x, where c_1 ,…
  43. 343.Solution of the differential equation [ x,dy = y( x - y )dx,,,0 < x < 2] is :
  44. 344.Let I be the purchase value of an equipment and V(t) be the value after it has been used f…
  45. 345.If [dy dx = y + 3 > 0,,] and y(0)=2, then [y( 2 )] is equal to :
  46. 346.The population p (t) at time t of a certain mouse species satisfies the differential equat…
  47. 347.At present, a firm is manufacturing 2000 items.
  48. 348.Let the population of rabbits surviving at time t be governed by the differential equation…
  49. 349.Let y(x) be the solution of the differential equation [( x, x )dy dx + y = 2x, x,( x 1 ).]…
  50. 350.If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation,…