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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)/(2x y)`, is given by `x^2 -y^2= c x`.

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To show that the family of curves for which the slope of the tangent at any point \((x, y)\) is given by \[ \frac{x^2 + y^2}{2xy} \] is represented by the equation ...
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NCERT-DIFFERENTIAL EQUATIONS-SOLVED EXAMPLES
  1. Find the equation of the curve passing through the point (1, 1) whose...

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  2. Find the general solution of the differential equation (dy)/(dx)-y=co...

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  3. Show that the family of curves for which the slope of the tangent at ...

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  4. Form the differential equation representing the family of ellipses ha...

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  5. Form the differential equation of the family of circles touching the ...

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  6. Form the differential equation representing the family of curves y = ...

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  7. Form the differential equation representing the family of curves y = ...

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  8. Verify that the function y=e^(-3x)is a solution of the differential eq...

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  9. Verify that the functiony = a cos x + b sin x, where, a, b in Ris a ...

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  10. Find the order and degree, if defined, of each of the following differ...

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  11. Form the differential equation representing the family of parabolas h...

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  12. Find the general solution of the differential equation (dy)/(dx)=(x+1...

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  13. Solve the differential equation (tan^(-1)y-x)dy=(1+y^2)dx.

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  14. Verify that the function y=c1e^(a x)cosb x+c2e^(a x)sinb x, where c1...

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  15. Form the differential equation of the family of circles in the second...

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  16. Find the particular solution of the differential equation log ((dy)/(d...

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  17. Solve the differential equation (x dy-y dx)ysin(y/x)=(y dx+x dy)xcos(...

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  18. Find the general solution of the differential equation x(dy)/(dx)+2y=...

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  19. Find the general solution of the differential equation y dx-(x+2y^2)d...

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  20. Find the particular solution of the differential equation (dy)/(dx)+y...

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