MHB Solve Cauchy Problem: Help Needed with Separate Variable Method

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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?
 
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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?

Is it surely $\frac{dx}{dr}$ ?
 

Thread 'Volterra equation of the second kind'

There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
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