# Differential Equation-Separable Equations

## 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.

## The Attempt at a Solution

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## 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.

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