The discussion focuses on solving the differential equation given by the equation xcos(x) = (2y + e^(3y)) y' with the initial condition y(0) = 0. The correct family of solutions is identified as xsin(x) + cos(x) = y^2 + e^(3y) + C, correcting a sign error from the initial attempt. Participants clarify the importance of substituting both x and y values into the equation based on the initial conditions provided, emphasizing the need to understand the roles of dependent and independent variables in different contexts.
PREREQUISITESStudents studying differential equations, educators teaching calculus, and anyone looking to deepen their understanding of initial value problems and their solutions.
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?