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Find the particular solution of the diff...

Find the particular solution of the differential equation `(1+y^(2))(1+logx)dx+xdy=0`, it is given that at `x=1`, `y=1`.

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The correct Answer is:
`log|x|+1/2(log x)^(2)= - tan^(-1)y+pi/4`
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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE 9 (f) Long Answer Type Questions (I)
  1. Solve the following initial value equations : x(1+y^(2))dx-y(1+x^(2)...

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  2. Solve the following differential equation: sqrt(1+x^2+y^2+x^2\ y^2)\ ...

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  3. Find the particular solution of the differential equation (1+y^(2))(1+...

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  4. Solve the following initial value equations : (dy)/(dx)=(1+y^(2))/(1...

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  5. Solve the following initial value equations : (1+e^(2x))dy+(1+y^(2))...

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  6. Solve the following initial value problems and find the corresponding ...

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  7. Solve the following initial value problem: x(dy)/(dx)+1=0; y(-1)=0

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  8. Solve the following initial value problems and find the corresponding ...

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  9. Solve the following initial value problems and find the corresponding ...

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  10. Solve the following initial value problems and find the corresponding ...

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  11. Solve the following initial value problems and find the corresponding ...

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  12. Find the particular solution of the following differential equation...

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  13. Find the particular solution of the following : (dy)/(dx)= 4 xy^(2),...

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  14. Find the particular solution of the following : (dy)/(dx)= y tan x, ...

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  15. Find the particular solution of the differential equation e^xsqrt(1-y^...

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  16. Find the particular solution of the following : (x+1)(dy)/(dx)=2e^(-...

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  17. Find the particular solution of the following : sec^(2)x tan y dx - ...

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  18. Find the particular solution of the following : (dy)/(dx)=x^(3) cose...

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  19. Find the particular solution of the following : (dy)/(dx)= (x(2 log ...

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  20. Find the particular solution of : (i) log(dy/dx)=2x+y (ii) log(d...

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