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Let y=f(x) be a curve passing through...

Let `y=f(x)` be a curve passing through `(1,1)` such that the triangle formed by the coordinate axes and the tangent at any point of the curve lies in the first quadrant and has area 2. Form the differential equation and determine all such possible curves.

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CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. The differential equation of the family of curves y=e^x(Acosx+Bsinx), ...

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  2. The differential equation whose solution is A x^2+B y^2=1 , where A an...

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  3. Let y=f(x) be a curve passing through (1,1) such that the triang...

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  4. The solution of the equation (dy)/(dx)=(x(2logx+1))/(siny+ycosy) is

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  5. The solution of the equation log ((dy)/(dx))=a x+b y is

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  6. If y=y(x) and (2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1, then y(pi/2) ...

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  7. The equation of the curves through the point (1, 0) and whose slope...

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  8. The solution of (d v)/(dt)+k/m v=-g is

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  9. The solution of the equation (dy)/(dx)=cos(x-y) is

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  10. The solution of the equation (x^2y+x^2)dx+y^2(x-1)dy=0 is given by

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  11. Solution of differential equation dy-sinxsiny dx=0 is

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  12. Solution of (dy)/(dx)+2x y=y is

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  13. The general solution of the differential equation (dy)/(dx)+sin((x+y)/...

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  14. The solution of (x d x+y dy)/(x dy-y dx)=sqrt((1-x^2-y^2)/(x^2+y^2)) ...

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  15. The curve for which the length of the normal is equal to the length ...

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  16. Identify the statement(s) which is/are true. (a) f( x , y )= e^( y...

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  17. The graph of the function y=f(x) passing through the point (0,1) a...

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  18. The solution of (dy)/(dx)=(a x+h)/(b y+k) represent a parabola whe...

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  19. The equation of the curve satisfying the differential equation y2 (x...

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  20. y=ae^(-1/x)+b is a solution of dy/dx=y/x^2,then (a)ainR (b)b=0 (c)b...

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