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Find the general solution of each of the following differential equations:
`(dy)/(dx) +((1+cos 2y))/((1-cos 2x)) =0`

Text Solution

Verified by Experts

The correct Answer is:
`tany =cot x +C`

`(dy)/(dx)+(2cos^(2)y)/(2sin^(2)x)=0 rArr (dy)/(dx)+("cosec"^(2)x)/(sec^(2)y)=0 rArr int (sec^(2)y)dy +int "cosec"^(2)xdx =C.`
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RS AGGARWAL-DIFFERENTIAL EQUATIONS WITH VARIABLE SEPARABLE-Exercise 19B
  1. Find the general solution of each of the following differential equat...

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  2. Find the general solution of each of the following differential equat...

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  3. Find the general solution of each of the following differential equat...

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  4. Find the general solution of each of the following differential equat...

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  5. Find the general solution of each of the following differential equati...

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  6. Find the general solution of each of the following differential equat...

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  7. Find the general solution of each of the following differential equat...

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  8. Find the general solution of each of the following differential equat...

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  9. Find the general solution of each of the following differential equat...

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

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

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  12. Find the particular solution of the differential equation log(dy)/(...

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  13. Solve the differential equation (x^(2)-yx^(2))dy +(y^(2)+x^(2)y^(2))dx...

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

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

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  16. Solve the differential equation (y)/(dx)=y sin 2x, " given that " y(0)...

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  17. Solve the differential equation (x+1)(dy)/(dx) =2xy, " given that " y(...

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  18. Solve (dy)/(dx)=x(2 log x +1), " given that " y =0 " when " x =2.

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  19. Solve (x^(3)+x^(2)+x+1)(dy)/(dx) =2x^(2)+x, " given that " y=1 " when ...

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  20. Solve (dy)/(dx)=y tan x, " given that " y=1 " when " x=0.

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