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The equation of the curve such that the...

The equation of the curve such that the distance between the origin and the tangent at an arbitrary point is equal to the distance between the origin and the normal at the same point is

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A DAS GUPTA-Differential Equation of the First Order-Exercise
  1. Show that the equation of the curve passing through the point (1,0) an...

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  2. Prove that the equation of a curve whose slope at (x,y) is -(x+y)/x an...

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  3. Find the equation of the curve such that the square of the intercept c...

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  4. Find the curves for which the length of normal is equal to the radius ...

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  5. Find the cartesian equation of the curves for which the length of the ...

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  6. Find the equation of the curve for which the length of the normal is c...

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  7. Find the equation of the curve which is such that the area of the rect...

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  8. The equation of the curve in which the portion of the tangent included...

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  9. The equation of the curve such that the distance between the origin a...

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  10. The normal PG to a curve meets the x-axis in G. If the distance of G f...

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  11. Find the equation of curves for which the cartesian subtangent varies ...

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  12. Find the equation of the curve in which the subnormal varies as the ...

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  13. Find the orthogonal trajectory of y^2=4a x (a being the parameter).

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  14. Prove that the family of curves x^2/(a^2+lambda)+y^2/(b^2+lambda)=1, w...

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  15. For the differential equation sqrt(1+(d^2y)/(dx^2))=x, the degree=and ...

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  16. If the general solution of a differential equation is (y+c)^2=cx, wher...

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  17. The general solution of dy/dx+(y(x+y))/x^2=0 is .

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  18. The solution of ( x + log y) dy + y dx=0 when y(0) =1 is :

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  19. Let d/(dx) (F(x))= e^(sinx)/x, x>0. If int1^4 2e^sin(x^2)/x dx = F(k)...

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  20. If x(t) is a solution of ((1+t)dy)/(dx)-t y=1 and y(0)=-1 then y(1)...

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