The discussion focuses on solving the Cauchy problem defined by the differential equation \(\frac{dx}{dr} = y\) with the initial condition \(x(0,s) = s\). Participants confirm that the method of separation of variables is applicable for this type of problem. The equation clearly indicates a first-order ordinary differential equation, and the initial condition provides a specific solution path. Clarification on the notation \(\frac{dx}{dr}\) is also sought, emphasizing the importance of precise mathematical representation.
PREREQUISITESMathematics students, educators, and anyone involved in solving differential equations or teaching related concepts will benefit from this discussion.
Julio said:Solve the Cauchy problem:
\begin{align}
\dfrac{dx}{dr} &= y\\
x(0,s) &= s
\end{align}
Help please, I don't remember how solve this :(. Separate variable isn't the method?