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Show that the family of curves for which...

Show that the family of curves for which the slope of the tangent at any point `(x,y)` on it is `(x^(2)+y^(2))/(2xy),` is given by `x^(2)-y^(2)=Cx `

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The correct Answer is:
`(y^(2) - x^(2)) = pm C_(1) x or x^(2) - y^(2) = Cx`.
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NCERT TAMIL-DIFFERENTIAL EQUATIONS-MISCELLANEOUS EXERCISE
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  3. For each of the exercises given below, verify that the given function...

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  5. Prove that x^(2)-y^(2)=c(x^(2)+y^(2))^(2) is the general solution of d...

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  6. Form the differential equation of the family of circles in the first q...

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  7. Find the general solution of the differential equation (dy)/(dx)+sqrt(...

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  8. Show that the general solution of the differential equation (dy)/(dx) ...

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  9. Find the equation of the curve passing through the point (0, (pi)/(4))...

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  10. Find the particular solution of the differential equation (1+e^(2x)...

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  11. Solve the differential equation y e^(x)/(y) dx = (x e^(x)/(y) + y^(2))...

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  12. Find a particular solution of the differential equation (x-y)(dx+dy)=d...

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  13. Solve the differential equation [(e^(-2sqrtx))/(sqrtx) - (y)/(sqrtx)](...

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  14. Find a particular solution of the differential equation (dy)/(dx)+ycot...

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  15. Find a particular solution of the differential equation (x+1)(dy)/(dx)...

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  16. The population of a village increases continuously at the rate proport...

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  17. The general solution of the differential equation (y dx - x dy)/(y ) =...

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  18. The general solution of a differential equation of the type (dy)/(dx)...

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  19. The general solution of the differential equation e^(x) dy + (y e^(x) ...

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