The discussion revolves around solving a differential equation involving separable variables, specifically the equation xcosx=(2y + e^(3y)) y' with the initial condition y(0)=0. Participants are exploring the implications of substituting values into the equation based on the initial condition.
Some guidance has been provided regarding the substitution of initial conditions, with participants clarifying the relationship between the variables in different contexts. There is an ongoing exploration of how to handle different initial conditions in related problems.
Participants are navigating the nuances of variable dependence in differential equations, particularly when transitioning between different problems with varying initial conditions.
Yes, substitute 0 for x and 0 for y. That's what y(0) = 0 means.neshepard said: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.
neshepard said: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?