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Differential Equation-Separable Equations

  • Thread starter neshepard
  • Start date
  • #1
67
0

Homework Statement


Find the solution of the diff eq that satisfies the given initial coordinate


Homework Equations


xcosx=(2y + e^(3y)) y' , y(0)=0


The Attempt at a Solution



So I have the family of solutions:
xsinx-cosx=y^2 + e^(3y)/3 + c

and I know to put 0 in for the x's, but the solution is wrong, and it appears like I need to put 0 into the y's (yes I did say y's) but not sure why.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
33,637
5,299

Homework Statement


Find the solution of the diff eq that satisfies the given initial coordinate


Homework Equations


xcosx=(2y + e^(3y)) y' , y(0)=0


The Attempt at a Solution



So I have the family of solutions:
xsinx-cosx=y^2 + e^(3y)/3 + c

and I know to put 0 in for the x's, but the solution is wrong, and it appears like I need to put 0 into the y's (yes I did say y's) but not sure why.
Yes, substitute 0 for x and 0 for y. That's what y(0) = 0 means.

You have a sign error in your solution. It should be xsinx + cosx = y^2 + e^(3y) + C.
 
  • #3
67
0
Thanks for the reply. And just to clarify, I have another problem where the initial condition is u(0)=-5 so I put in -5 for my x's and 0 for my y's?
 
  • #4
fzero
Science Advisor
Homework Helper
Gold Member
3,119
289
Thanks for the reply. And just to clarify, I have another problem where the initial condition is u(0)=-5 so I put in -5 for my x's and 0 for my y's?
If x is the dependent variable, that is, you have u(x), then you need to set x=0 and u=-5. You don't have x and y anymore, one of them has been replaced by a new function u in this other problem.
 
  • #5
67
0
Nice...thanks.
 

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