SOLUTION: solve the differential equation: y dy/dx = x(y^4 + 2(y)^2 + 1) at x= -3 , y=1

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Question 1167011: solve the differential equation:
y dy/dx = x(y^4 + 2(y)^2 + 1) at x= -3 , y=1
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!




Initial condition:







or

No solution for .











John

My calculator said it, I believe it, that settles it


I > Ø
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

     =   at x= -3 , y=1     (1)


Use the method of separation of variables.


Collect all the term with y and dy on the left side; all the terms with x and dx on the right side


     = .


     = 


     = 


Take antiderivative; do not forget to introduce an arbitrary constant C


    - =  + C       (2)


Find the value of the constant C from initial conditions


    - =  + C;


    - = 9 + C;  C = - 9  = .


Substitute  C =  into (2)


    - =  - 


    - = 


     = 


     =  - 1 =  = 


    y = .      ANSWER

Solved.



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