#413 Consider the ODE xy + 2y + xy = 0

Consider the ODE xy + 2y + xy = 0 - Math

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Free Chegg Question

Consider the ODE  

Rewrite the given ODE as,

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Free Chegg Answer

1. Step 1 of 8

   Consider the ODE  

   Rewrite the given ODE as,

   

   Let be the solution of the given equation.

   So,

   

   Differentiating with respective,

   

   Differentiating with respective,

   

2. Step 2 of 8

   Substitute in equation (1),

   

   

   

   Compare the coefficient of  on both sides,

   

   Compare the coefficient of  on both sides,

   

   Compare the coefficient of  on both sides,

   

3. Step 3 of 8

   Case1:

   Let’s take  (from the equation (3)).

   Substitute in the equation (4),

   

   For, the value is

   

    

4. Step 4 of 8

   For, the value is

    

   

   For, the value is

   

   For, the value is

   

   And so on.

5. Step 5 of 8

   Substitute these values into,

    

   

6. Step 6 of 8

   Multiply and divide the equation (5) by,

   

   Plug  in the above series,

   

   Hence, the series is.

7. Step 7 of 8

   Case 2:

   Let’s take and  (from the equation – (3)).

   Substitute in the equation – (4),

   

   For  the value is,

   

   For  the value is,

   

   For  the value is,

   

   For  the value is,

   

   And so on.

8. Step 8 of 8

   Substitute these values into,

   

   

   Plug  in the above series,

   

   Hence, the series is.