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Differential Equations

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  1. 251.For x0, y=y(x) solves (x+1),dy=((x+1)^2+y-3),dx, y(2)=0.
  2. 252.Let y=y(x) solve (y^2-x)dydx=1, y(0)=1.
  3. 253.The differential equation of the family of curves x^2=4b(y+b), bR, is:
  4. 254.If f'(x)=^-1( x+ x), -/2<x</2, f(0)=0, then f(1) equals:
  5. 255.If dydx=xyx^2+y^2, y(1)=1; a value of x satisfying y(x)=e is:
  6. 256.Let f(x)=((^-1x)+(^-1x))^2-1, |x|>1.
  7. 257.Let y=y(x) solve √1-x^2dydx+√1-y^2=0, |x|<1.
  8. 258.If y=y(x) solves e^y-x(dydx) (schematic: dy-dxe^y-x=xdx), with y(0)=0, then y(1) equals:
  9. 259.The general solution of √1+x^2+y^2+x^2y^2+xydydx=0 is (C constant):
  10. 260.If y=(2x-1) x solves dydx+p(x)y=2 x, 0<x</2, then p(x) equals:
  11. 261.If y=y(x) solves (5+e^x)^2dydx (schematic: (5+e^x),dy/(2+y)=-e^x,dx), y(0)=1, then a value…
  12. 262.The solution of dydx-y+3x_e(y+3x)+3=0 is (C constant):
  13. 263.Let f:(0,)(0,) be differentiable, f(1)=e, and _t xt^2f^2(x)-x^2f^2(t)t-x=0.
  14. 264.The solution curve of (1+e^-x)(1+y^2)dydx=y^2, through (0,1), is:
  15. 265.If x^3,dy+xy,dx=x^2,dy+2y,dx, y(2)=e, x>1, then y(4) equals:
  16. 266.Let y=y(x) solve (2+ x)(y+1)dydx=- x, y>0, y(0)=1.
  17. 267.If a curve y=f(x), through (1,2), solves 2x^2,dy=(2xy+y^2),dx, then f(12) is:
  18. 268.Let y=y(x) solve xdydx+2y x=2x, x(0,/2).
  19. 269.Let y=y(x) solve xy'-y=x^2(x x+ x), x>0.
  20. 270.If y=y(x) solves xdydx+2y=x^2, y(1)=1, then y(12) is:
  21. 271.Let f:[0,1]R satisfy f(xy)=f(x)f(y), f(0)0.
  22. 272.If dydx+3^2xy=1^2x, x(-3,3), y(4)=43, then y(-4) equals:
  23. 273.The curve amongst (x^2-y^2),dx+2xy,dy=0 passing through (1,1) is:
  24. 274.Let f satisfy f'(x)=7-34f(x)x, x>0, f(1)4.
  25. 275.The solution of dydx=(x-y)^2, y(1)=1, is:
  26. 276.If y(x) solves dydx+2x+1xy=e^-2x, x>0, y(1)=12e^-2, then:
  27. 277.Let y=y(x) solve xdydx+y=x_ex, x>1.
  28. 278.If a curve passes through (1,-2) and has slope x^2-2yx, it also passes through:
  29. 279.The general solution of (y^2-x^3),dx-xy,dy=0, x0, is (C constant):
  30. 280.If xdydx-y x=6x, 0<x</2, y(/3)=0, then y(/6) equals:
  31. 281.The slope of the tangent to y=y(x) at (x,y) is 2yx^2.
  32. 282.Consider y^2,dx+(x-1y)dy=0.
  33. 283.If y=y(x) solves dydx=( x-y)^2x, x(-2,2), y(0)=0, then y(-4) is:
  34. 284.Let y=y(x) solve dydx+y x=2x+x^2 x, x(-2,2), y(0)=1.
  35. 285.The solution of xdydx+2y=x^2 (x0) with y(1)=1 is:
  36. 286.Let y=y(x) solve (x^2+1)^2dydx+2x(x^2+1)y=1, y(0)=0.
  37. 287.The differential equation for the family of ellipses (foci on either axis, centre at origi…
  38. 288.The curve satisfying (x^2-y^2),dx+2xy,dy=0, through (1,1), is:
  39. 289.Let y=y(x) solve xdydx+y x=4x, x(0,).
  40. 290.Let y=y(x) solve dydx+2y=f(x), f(x)=1 for x[0,1], 0 otherwise, y(0)=0.
  41. 291.If (2+ x)dydx+(y+1) x=0, y(0)=1, then y(2) is:
  42. 292.The curve satisfying y,dx-(x+3y^2)dy=0, through (1,1), also passes through:
  43. 293.If a curve y=f(x) passes through (1,-1) and satisfies y(1+xy),dx=x,dy, then f(-12) is:
  44. 294.If f(x) is differentiable on (0,), f(a)=1, and _t xt^2f(x)-x^2f(t)t-x=1 for each x>0, then…
  45. 295.The solution of dydx+y2 x= x2y, 0 x</2, y(0)=1, is given by:
  46. 296.The solution of y,dx-(x+2y^2),dy=0 is x=f(y).
  47. 297.If y(x) solves (x+2)dydx=x^2+4x-9, x-2, y(0)=0, then y(-4) is:
  48. 298.Let y(x) solve (x x)dydx+y=2x x, x1.
  49. 299.If the differential equation representing the family of circles touching the x-axis at the…
  50. 300.Let population p(t) satisfy dp(t)dt=12p(t)-200, p(0)=100.