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Differential Equations

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  1. 201.If the solution curve of dydx=x+y-2x-y passes through (2,1) and (k+1,2), k>0, then:
  2. 202.Let y=y(x) solve dydx+2x^2+11x+13x^3+6x^2+11x+6y = x+3x+1, x>-1, passing through (0,1).
  3. 203.The population P=P(t) at time t of a species follows dPdt=0.5P-450.
  4. 204.Let f be twice differentiable on R, f(0)=1, f'(0)=2, f''(x)0.
  5. 205.The difference between degree and order of the differential equation representing y^2=a(x+…
  6. 206.The slope of the tangent to a curve at P(x,y) is xy^2+yx.
  7. 207.Let f(x)=_0^x e^tf(t),dt+e^x be differentiable for all x.
  8. 208.Bacteria population grows proportionally; p(0)=1000, increases 20% in 2h.
  9. 209.If y=y(x) solves e^ y ydydx+e^ y x= x, y(0)=0, then 1+y(6)+√32y(3)+1√2y(4) is ______.
  10. 210.If a curve passes through the origin and the slope of the tangent at (x,y) is x^2-4x+y+8x-…
  11. 211.If the curve y=y(x) satisfying (2xy^2-y),dx+x,dy=0 passes through the intersection of 2x-3…
  12. 212.If y=f(x) passes through (1,2) and satisfies xdydx+y=bx^4, for what b is _1^2 f(x),dx=625?
  13. 213.*(Content of question 151 duplicated the previous problem's solution in the source; retain…
  14. 214.Let y=y(x) solve x,dy-y,dx=(x^2-y^2),dx, x1, y(1)=0.
  15. 215.Which is true for y(x) satisfying dydx=xy-1+x-y, y(0)=0:
  16. 216.Let y=y(x) solve dydx=2(x+1).
  17. 217.Let C_1 solve 2xydydx=y^2-x^2, x>0; let C_2 solve 2xy=x^2-y^2dy/dx(schematic).
  18. 218.Let y=y(x) solve dydx=(y+1)[(y+1)e^x^2/2-x], 0<x<2, y(2)=0.
  19. 219.Let y=y(x) solve x(3 x+ x+3),dy = [1+y x(3 x+ x+3)],dx, 0 x/2, y(0)=0.
  20. 220.The curve y=y(x) solves 2(x^2+x^5/4),dy-y(x+x^1/4),dx=2x^9/4,dx, x>0, passing through (1,1…
  21. 221.If y=y(x) solves dydx+2y x= x, y(3)=0, the maximum value of y(x) over R is:
  22. 222.If y=y(x) solves dydx+( x)y= x, 0 x/3, y(0)=0, then y(4) is:
  23. 223.*(Vector geometry --- not a differential equation; included as it appears in the source un…
  24. 224.Let y=y(x) solve dydx=1+xe^y-x, -√2<x<√2, y(0)=0.
  25. 225.Let y=y(x) solve _edydx=3x+4y, y(0)=0.
  26. 226.If y=y(x), y(0,2), solves ydydx-(x+y)-(x-y)=0, y(0)=0, then 5y'(2) is ______.
  27. 227.Let y=y(x) solve (x-x^3),dy=(y+yx^2-3x^4),dx, x>2.
  28. 228.Let y=y(x) solve dy=e^ x+y,dx, N.
  29. 229.Let y=y(x) solve x,dy=(y+x^3 x),dx, y()=0.
  30. 230.Let a curve y=f(x) pass through (2,(_e2)^2) and have slope 2yx_ex.
  31. 231.Let y=y(x) solve (x+2)e^(y+1)/(x+2),dx + (y+1),dx = (x+2),dy, y(1)=1.
  32. 232.Let y=y(x) solve x!(yx)dy = [y!(yx)-x]dx, -1 x1, y!(12)=6.
  33. 233.Let y=y(x) solve e^x√1-y^2,dx+yx,dy=0, y(1)=-1.
  34. 234.Let a curve y=y(x) solve (12^-1(e^-x))dx = e^2x (schematic; see source), intersecting the …
  35. 235.Let y=y(x) solve e^ydydx-2e^y x+ x^2x=0, y(2)=0.
  36. 236.Let y=y(x) solve ^2x,dy+2,dx=(1+y2x)^2x,dx, y(4)=0.
  37. 237.Let y=y(x) solve dydx-|A|=0 for x>0, where A=pmatrixy x&10&-1pmatrix (schematic 33 determi…
  38. 238.*(Vector algebra, not differential equations --- included as extracted.)* Let a= i- j+ k, …
  39. 239.A differential equation representing parabolas with axis parallel to the y-axis, whose lat…
  40. 240.Let f0 on [0,1], twice differentiable on (0,1).
  41. 241.If dydx=2^x+y-2x^22^x2^y, y(0)=1, then y(1) is:
  42. 242.If dydx=2^xy+2y2x^22^x+2x+y_e2 (schematic), y(0)=0, then for y=1, x lies in:
  43. 243.If ydydx=x[y^2x^2+(y^2x^2)]!/'!(y^2x^2), x>0, >0, y(1)=-1, then (y^24) is:
  44. 244.Let y=y(x) solve dydx=2(y+2 x-5)x-2 x, y(0)=7.
  45. 245.Let y(x) solve 2x^2,dy+(e^y-2x),dx=0, x>0, y(e)=1.
  46. 246.Let y=f(x) pass through (-2,2); the slope at (x,f(x)) is given by f(x)+xf'(x)=x^2.
  47. 247.If the solution curve of (2x-10y^3),dy+y,dx=0 passes through (0,1) and (2,), then is a roo…
  48. 248.Let y=y(x) solve (y+1)^2x,dx+ x,dy+y,dx=0, x(0,2).
  49. 249.*(Vector algebra --- not a differential equation; included as extracted.)* Let a, b, c be …
  50. 250.If y=y(x) solves x^2,dy+(y-1x)dx=0, x>0, y(1)=1, then y(12) is: