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Prove that x^(2)-y^(2)=c(x^(2)+y^(2))^(2...

Prove that `x^(2)-y^(2)=c(x^(2)+y^(2))^(2)` is the general solution of differential equation `(x^(3)-3xy^(2))dx=(y^(3)-3x^(2)y)dy,` where `c` is a parameter.

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NEW JOYTHI PUBLICATION-DIFFERENTIAL EQUATIONS-NCERT MISCELLANEOUS EXERCISE
  1. For each of the differential equations given below, indicate its order...

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

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

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

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

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  6. Form the differential equation representing the family of curves given...

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

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

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

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

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

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  12. Solve the differential equation ye^(x/y)dx=(xe^(x/y)+y^(2))dy(yne0).

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

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

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

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

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

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  18. The general solution of the differential equation (ydx-xdy)/(x)=0 is

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

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  20. The general solution of the differential equation e^(x)dy+ydx=0 is

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