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Find the general solution of the differ...

Find the general solution of the differential equation `(dy)/(dx)+sqrt((1-y^2)/(1-x^2))=0`.

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`(dy)/(dx)=-sqrt((1-y^(2))/(1-x^(2)))`
`implies (dy)/(sqrt(1-y^(2)))=-(dx)/(sqrt(1-x^(2)))`
`implies int(dy)/(sqrt(1-y^(2)))+int(dx)/(sqrt(1-x^(2)))=c`
`implies sin^(-1)y+sin^(-1)x=c`
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NAGEEN PRAKASHAN ENGLISH-DIFFERENTIAL EQUATIONS-Miscellaneous Exercise
  1. For each of the differential equations given below, indicate its orde...

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

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

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

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

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

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  7. Show that the general solution of the differentia equation (dy)/(dx...

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

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

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

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

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

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

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

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

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

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

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

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