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Differential Equations

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  1. 101.Let y=y(x) be the solution of the differential equation [x(dy)/(dx) - 2y = x^3(2-x^3)^2 y,…
  2. 102.Let y=y(x) be the solution of the differential equation xdydx-y=x^2 x, x(0,), y!(()/(2))=2…
  3. 103.Let y=y(x) be the solution of the differential equation [(1+ x)(dy)/(dx)+(y+1) x=0, y(0)=0…
  4. 104.Let y=y(x) be the solution of the differential equation [(dy)/(dx) = (1+x+x^2)(1-y+y^2), y…
  5. 105.Let y=y(x) be the solution of [(dy)/(dx)+(6x^2+(3x^2+2x^3+4)e^-2x(x^3+2)(2+e^-2x))y = 2+e^…
  6. 106.Let f:RR be such that f(xy)=f(x)f(y) for all x,yR and f(0) 0.
  7. 107.Let y=y(x) be the solution of the differential equation [x√1-x^2,dy + (y√1-x^2-x^-1x),dx=0…
  8. 108.If the area of the region (x,y): 1-2x y 4-x^2, x0, y0 is , ,N, (,)=1, then + is:
  9. 109.Let A_1 be the bounded area enclosed by the curves y=x^2+2, x+y=8 and the y-axis in the fi…
  10. 110.The area of the region R=(x,y): xy27, 1 y x^2 is:
  11. 111.Let f:(1,)R, f(x)=x-1x+1.
  12. 112.Let f be a differentiable function such that f^2(x+2) = 2f(x)-3(x+2)^2 = 10_0^x(t+2)f(t),d…
  13. 113.If y=y(x) is the solution of √4-x^2dydx = ((^-1(x/2))^2-y)^-1(x/2), -2 x2, y(2)=^24-2, the…
  14. 114.Let y=y(x) be the solution of the differential equation [(dy)/(dx)+2y^2x = 2^2x+3 x^2x, y(…
  15. 115.Let f:RR satisfy f(x+y)=f(x)f(y) for all x,yR, f'(0)=4a, and f satisfies f''(x)-3af'(x)-f(…
  16. 116.Let x=x(y) be the solution of the differential equation [y^2,dx+(x-1y)dy=0, x(1)=1.] Then …
  17. 117.If x=f(y) is the solution of (1+y^2)+(x-2e^^-1y)dydx=0, y(-2,2), with f(0)=1, then f!(1√3)…
  18. 118.Let a curve y=f(x) pass through (0,5) and (_e2,k).
  19. 119.Let x=x(y) be the solution of y=(x-ydxdy)xy, y>0, x(1)=2.
  20. 120.Let y=y(x) be the solution of (xy-5x^2√1+x^2),dx+(1+x^2),dy=0, y(0)=0.
  21. 121.Let y=f(x) for some function f, satisfy _0^x tf(t),dt = x^2f(x), x>0, and f(2)=3.
  22. 122.Let y=y(x) be the solution of x(_e( x))^2,dy+( x-3y x_e( x)),dx=0, x(0,/2).
  23. 123.If for the solution curve of dydx+( x)y=2+ x(1+2 x)^2, x(-2,2), f!(3)=√310, then f!(4) is …
  24. 124.Let g be a differentiable function such that _0^x g(t),dt = x-_0^x t,g(t),dt, x0, and let …
  25. 125.Let y=y(x) be the solution of dydx+3^2x,y+3y=^2x, y(0)=13+e^3.
  26. 126.If a curve y=y(x) passes through (1,2) and satisfies (7x^4 y-e^x y)dxdy=x^5, x1, then at x…
  27. 127.Let y=y(x) be the solution curve of x(x^2+e^x),dy+(e^x(x-2)y-x^3),dx=0, x>0, passing throu…
  28. 128.Let y=y(x) be the solution of (x^2+1)y'-2xy=(x^4+2x^2+1) x, y(0)=1.
  29. 129.Let x=x(t) and y=y(t) be solutions of dxdt+ax=0 and dydt+by=0, a,bR.
  30. 130.If the solution of (2x+3y-2),dx+(4x+6y-7),dy=0, y(0)=3, is x+ y+3_e|2x+3y-|=6, then +2+3 i…
  31. 131.If y=y(x) is the solution curve of (x^2-4),dy-(y^2-3y),dx=0, x>2, y(4)=32, and the slope o…
  32. 132.If the solution curve of dydx=x+y-2x-y passing through (2,1) is [^-1!((y-1)/(x-1))-(1)/()_…
  33. 133.A function y=f(x) satisfies f(x)2x+ x-(1+^2x)f'(x)=0, f(0)=0.
  34. 134.If the solution curve y=y(x) of (1+y^2)(1+_ex),dx+x,dy=0, x>0, passes through (1,1) and y(…
  35. 135.If (yx)=_e|x|+2 is the solution of x(yx)dydx=y(yx)+x and y(1)=3, then ^2 is equal to:
  36. 136.Let y=y(x) be the solution of (1-x^2),dy = [xy+(x^3+2)√3(1-x^2)]dx, -1<x<1, y(0)=0.
  37. 137.Let y=y(x) be the solution of x,dy+2(1-x) x+x(2-x),dx=0, y(0)=2.
  38. 138.The solution curve of ydxdy=x(_ex-_ey+1), x>0,y>0, passing through (e,1), is:
  39. 139.Let y=y(x) solve dydx= x+y x( x- x x), x(0,2), y(4)=2.
  40. 140.The temperature T(t) of a body at t=0 is 160^ F and decreases per dTdt=-K(T-80), K>0.
  41. 141.Let y=y(x) solve ^2x,dx+(e^2y2x+ x),dy=0, 0<x<2, y(4)=0.
  42. 142.Let y=y(x) solve dydx=2x(x+y)^3-x(x+y)-1, y(0)=1.
  43. 143.If x=x(t) solves (t+1),dx=(2x+(t+1)^4),dt, x(0)=2, then x(1) equals ______.
  44. 144.Let be a non-zero real number.
  45. 145.Let y=y(x) solve x^3,dy+(xy-1),dx=0, x>0, y(12)=3-e.
  46. 146.Let y=y(x) solve (x^2-3y^2),dx+3xy,dy=0, y(1)=1.
  47. 147.Let y=y(x) solve dydx=yx(1+xy^2(1+_ex)), x>0, y(1)=3.
  48. 148.Let y=y(t) solve dydt+ y= e^- t, ,,>0.
  49. 149.Let y=f(x) solve y(x+1),dx-x^2,dy=0, y(1)=e.
  50. 150.Let y=y(x) solve x_exdydx+y=x^2_ex, x>1.