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Solve the differential equation: (1+x^2)...

Solve the differential equation: `(1+x^2) dy/dx + y = tan^-1 x`

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The correct Answer is:
`y=(tan^(-1)x-1)+ce^(-tan^(-1)x)`.
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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE 9 (i) Long Answer Type Questions (I)
  1. Find the general solution of the following differential equations (x...

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  2. Solve the following differential equations : (dy)/(dx)-(2x)/(1+x^(2...

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  3. Find the general solution of the following differential equations (1...

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  4. Solve: (1+x^2)(dy)/(dx)+2xy=cosx

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  5. (1-x^2) dy/dx-xy=1

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  6. y dx+(x-y^2)dy=0

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  7. y dx - (x + 2y^(2)) dy = 0

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

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  9. Solve the following differential equations : (dy)/(dx)-y/x=((x-1)/(...

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  10. Solve the following initial value problems : (dy)/(dx)=2x+y, given t...

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  11. Solve the following initial value problems : x(dy)/(dx)+y=x^(3),y(2)...

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  12. Solve the following initial value problems : x(dy)/(dx)+2y=x^(2),y(1...

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  13. Solve the following initial value problems : x (dy)/(dx)+2y=x^(2)(x ...

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  14. Solve each of the following initial value problem: x(dy)/(dx)+y=xcosx+...

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  15. Solve each of the following initial value problem: (dy)/(dx)=2ytanx=si...

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  16. dy/dx+y tan x= sec x.

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  17. Solve the differential equation (dy)/(dx)-3ycotx=sin2x given y=2 when ...

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  18. Solve the following initial value problems : cos^(3)x (dy)/(dx)-y si...

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  19. Solve the following initial value problems : y e^(y)dx=(y^(3)+2x e^(...

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  20. Find the particular solution of differential equation (dy)/(dx)=(x+yc...

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