Differential Equation-Separable Equations

[neshepard]

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.

 

[Mark44]

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.

 

[neshepard]

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?

 

[fzero]

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 You don't have x and y anymore, one of them has been replaced by a new function u in this other problem.

 

[neshepard]

Nice...thanks.