Linear First Order ODE/dy = f(x) dx/Examples

Examples of Linear First Order ODE: $\d y = \map f x \rd x$

Example: $y' = e^{-x^2}$

The linear first order ODE:

$(1): \quad \dfrac {\d y} {\d x} = e^{-x^2}$

has the general solution:

$y = \dfrac {\sqrt \pi} 2 \map {\erf} x + C$

where $\erf$ denotes the error function.