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Differential Equations

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  1. 151.Let the solution curve y=y(x) of dydx-3x^5^-1(x^3)(1+x^6)^3/2y = 2x(x^3-^-1x^3)(1+x^6) pas…
  2. 152.The solution of dydx=-x^2+3y^23x^2+y^2, y(1)=0 is:
  3. 153.Let y=y(x) solve (3y^2-5x^2)y,dx+2x(x^2-y^2),dy=0, y(1)=1.
  4. 154.If y=y(x) is the solution curve of dydx+y x = x x, 0 x3, y(0)=1, then y(6) is:
  5. 155.Let x=(x^ y^) be the solution of 2x^2y,dy-(1-xy^2),dx=0, x>0, y(2)=_e2.
  6. 156.Let y=y(x) solve (x x),dy+(xy x+y x-1),dx=0, 0<x<2.
  7. 157.If the solution curve f(x,y)=0 of (1+_ex)dxdy-x_ex=e^y, x>0, passes through (1,0) and (,2)…
  8. 158.Let the solution curve x=x(y), 0<y<2, of (_e( y))^2 y,dx-(1+3x_e( y)) y,dy=0 satisfy x(3)=…
  9. 159.Let f be a differentiable function such that x^2f(x)-x=4_0^x tf(t),dt, f(1)=23.
  10. 160.Let the tangent at any point P on a curve passing through (1,1) and (110,100) intersect th…
  11. 161.Let y=y(x) solve (1-x^2y^2),dx=y,dx+x,dy.
  12. 162.Let y=y(x) solve dydx+5x(x^5+1)y = (x^5+1)^2x^7, x>0, y(1)=2.
  13. 163.Let y=y(x), y>0, solve (1+x^2),dy=y(x-y),dx.
  14. 164.Let y=y_1(x) and y=y_2(x) solve dydx=y+7 with y_1(0)=0, y_2(0)=1.
  15. 165.If y=y(x) solves dydx+4xx^2-1y = x+2(x^2-1)^5/2, x>1, with y(2)=29_e(2+√3) and y(√2)=_e(+)…
  16. 166.Let x=x(y) solve 2(y+2)_e(y+2),dx+(x+4-2_e(y+2)),dy=0, y>-1, with x(e^4-2)=1.
  17. 167.The slope of normal at (x,y), x,y>0, on y=y(x) is x^2xy-x^2y^2-1.
  18. 168.Let y=y(x) solve (x+1)y'-y=e^3x(x+1)^2, y(0)=13.
  19. 169.Let y=y(x) solve y^2,dx+(x^2-xy+y^2),dy=0, passing through (1,1), and intersects y=√3x at …
  20. 170.If y=y(x) solves 2x^2dydx-2xy+3y^2=0 with y(e)= e3, then y(1) is:
  21. 171.Let the solution curve y=y(x) of (4+x^2),dy-2x(x^2+3y+4),dx=0 pass through the origin.
  22. 172.Let S=(0,2)-2,34,32,74.
  23. 173.If the solution of dydx+e^x(x^2-2)y=(x^2-2x)(x^2-2)e^2x satisfies y(0)=0, then y(2) is:
  24. 174.Let dydx=ax-by+abx+cy+a, where a,b,c are constants, represent a circle through (2,5).
  25. 175.If dydx+2^x-y(2^y-1)2^x-1=0, x,y>0, y(1)=1, then y(2) equals:
  26. 176.If the solution curve of ((^-1y)-x),dy=(1+y^2),dx passes through (1,0), the abscissa of th…
  27. 177.Let y=y(x) solve (1-x^2),dy = [xy+(x^3+2)√1-x^2]dx, -1<x<1, y(0)=0.
  28. 178.Let the solution curve y=y(x) of [(xx^2-y^2+e^y/xx)dx = (x^2+xx^2-y^2+e^y/xy)dy (schematic…
  29. 179.Let y=y(x) solve x(1-x^2)dydx+(3x^2y-y-4x^3)=0, x>1, y(2)=-2.
  30. 180.Let x=x(y) solve 2ye^x/y^2,dx+(y^2-4xe^x/y^2),dy=0, x(1)=0.
  31. 181.Let the solution curve of xdydx-y=y^2+16x^2, y(1)=3, be y=y(x).
  32. 182.Let y=y(x) solve dydx+√2,y2^4x-2x = xe^^-1(√22x), 0<x<2, with y(4)=^232.
  33. 183.If y=y(x) solves (1+e^2x)dydx+2(1+y^2)e^x=0 and y(0)=0, then 6(y'(0)+(y(_e√3))^2) is:
  34. 184.Let y=y(x), x>1, solve (x-1)dydx+2xy=1x-1, y(2)=1+e^42e^4.
  35. 185.If x=x(y) solves ydxdy=2x+y^3(y+1)e^y, x(1)=0, then x(e) is:
  36. 186.The slope of the tangent to C:y=y(x) at (x,y) is 2e^2x-6e^-x+92+9e^-2x.
  37. 187.The general solution of (x-y^2),dx+y(5x+y^2),dy=0 is (where c is a constant):
  38. 188.Let a smooth curve y=f(x) have slope of tangent directly proportional to -yx.
  39. 189.Let y=y(x) solve dydx=4y^3+2yx^23xy^2+x^3, y(1)=1.
  40. 190.If dydx+2y x= x, 0<x<2, y(3)=0, then the maximum value of y(x) is:
  41. 191.Let a curve y=y(x) pass through (3,3), and the area under the curve from 3 to x (x>3) be y…
  42. 192.Let the solution curve y=f(x) of dydx+xyx^2-1=x^4+2x1-x^2, x(-1,1), pass through the origi…
  43. 193.Suppose y=y(x) solves dydx-y=2-e^-x such that _xy(x) is finite.
  44. 194.Let y_1(x), y_2(x) solve dydx=x+y with y_1(0)=0, y_2(0)=1.
  45. 195.Let y=y(x) solve (2x^2)_e(x^2) (schematic) dy+4xy-4√2x(x^2-4)dx=0, 0<x<2, through (6,1).
  46. 196.Let the solution curve of x,dy=(x+x^2+y^2+y)dx, x>0, intersect x=1 at y=0 and x=2 at y=.
  47. 197.If y=y(x), x(0,/2), solves ^2(2x)dydx+(8^2(2x)+24x)y = 2e^-4x(22x+2x), with y(4)=e^-, then…
  48. 198.Let y=y(x) solve dydx+1x^2-1y = (x-1x+1)^1/2, x>1, passing through (2,13).
  49. 199.The differential equation of the family of circles through (0,2) and (0,-2) is:
  50. 200.Let y=y(x) solve (1+e^2x)dydx+y=1, passing through (0,2).