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The differential equation of family of curves `x^(2)+y^(2)-2ax=0`, is

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`x^(2)+y^(2)-2ax=0` ………..`(1)`
Differntitate with respect to `x`
`2x+2y(dy)/(dx)-2a=0`
`implies a=x+y(dy)/(dx)`
From eq. `(1)`
`x^(2)+y^(2)-2x(x+y(dy)/(dx))=0`
`implies y^(2)-x^(2)-2xy(dy)/(dx)=0`
whichis the required differential equations.
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NAGEEN PRAKASHAN ENGLISH-DIFFERENTIAL EQUATIONS-Miscellaneous Exercise
  1. The differential equation of family of curves x^(2)+y^(2)-2ax=0, is

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  2. For each of the differential equations given below, indicate its orde...

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  3. For each of the exercises given below, verify that the given function...

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  4. Form the differential equation representing the family of curves give...

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

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  6. Form the differential equation of the family of circles in the firs...

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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 differentia equation (dy)/(dx...

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

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

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  11. Solve the differential equation y e^(x/y)dx=(x e^(x/y)+y^2)dy(y!=0)

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

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  13. Solve the differential equation [(e^(-2sqrt(x)))/(sqrt(x))-y/(sqrt(x)...

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

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  15. find the particular solution satisfying the given condition, for the f...

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

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  17. The general solution of the differential equation (y dx-x dy)/y=0 is...

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

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  19. Solve: e^(x)(x+1)dx+(ye^(y)-xe^(x))dy=0, such that f(0)=0

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