The discussion revolves around finding the general solution for the differential equation y' + ay = 0, which falls under the subject area of differential equations. Participants are exploring the correct form of the solution and the implications of constants involved.
The discussion is active, with participants seeking clarification on the correct form of the solution and the significance of the constant. There is no explicit consensus yet, as multiple interpretations of the solution are being explored.
Participants are navigating the implications of constants in the solution and questioning assumptions about the uniqueness of the solution based on the value of "c".
Math10 said:Homework Statement
Find the general solution of y'+ay=0.
Homework Equations
dy/dx=-ay
dy/y=-a dx
∫ dy/y=∫ -a dx
ln(y)=-ax+C
y=e^(-ax)
The Attempt at a Solution
What I want to know is that is y=e^(-ax) the answer or y=ce^(-ax) is the answer?
Okay, and now you solve for y by taking the exponential of both sides.Math10 said:Homework Statement
Find the general solution of y'+ay=0.Homework Equations
dy/dx=-ay
dy/y=-a dx
∫ dy/y=∫ -a dx
ln(y)=-ax+C
? What happened to the "C"?y=e^(-ax)
The Attempt at a Solution
What I want to know is that is y=e^(-ax) the answer or y=ce^(-ax) is the answer?