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Find the curves for which the length of ...

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

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Find the curve for which the length of normal is equal to the radius vector.

The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

The differential equation of the family of curves for which the length of the normal is equal to a constant k, is given by

Find the curve in which the length of the normal varies as the square of the ordinate.

Find the equation of the curve for which the length of the normal is constant and the curves passes through the point (1,0).

If the length of the normal for each point on a curve is equal to the radius vector,then the curve (a) is a circle passing through origin (b) is a circle having centre at origin and radius 0 (c) is a circle having centre on x-axis and touching y-axis (iv) is a circle having centre on y-axis and touching x-axis

Find the cartesian equation of the curves for which the length of the tangent is of constant length.

Find the curve for which the perpendicular from the foot of the ordinate to the tangent is of constant length.

At any point on the curve 2x^(2)y^(2)-x^(4)=c, the mean proportional between the abscissa and the difference between the abscissa and the sub-normal drawn to the curve at the same point is equal to ordinate (b) radius vector x-intercept of tangent ( d) sub-tangent

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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