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Show that the equation of the curve passing through the point `(1,0)` and satisfying the differential equation `(1+y^2)dx-xydy=0` is `x^2-y^2=1`

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A DAS GUPTA-Differential Equation of the First Order-Exercise
  1. A radioactive substance is subject to the law of natural decay (dv)/(d...

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  2. A country has a food deficit of 10%. Its population grows continuously...

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  3. Show that the equation of the curve passing through the point (1,0) an...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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