${\displaystyle y=y'={\frac {\mathrm {d} y}{\mathrm {d} x}}}${\displaystyle y=y'={\frac {\mathrm {d} y}{\mathrm {d} x}}}

This equation imposes a constraint on potential solutions of the equation: The greater a function value will be, the greater the slope must be.

The plot shows four solutions of the equation which have all a representation of the kind

${\displaystyle y=C\cdot \mathrm {e} ^{x}}${\displaystyle y=C\cdot \mathrm {e} ^{x}}

namely

${\displaystyle C_{\text{red}}=1,\quad C_{\text{green}}=\mathrm {e} ^{1.1},\quad C_{\text{yellow}}=\mathrm {e} ^{-2},\quad C_{\text{blue}}=-\mathrm {e} ^{-3/2},円}${\displaystyle C_{\text{red}}=1,\quad C_{\text{green}}=\mathrm {e} ^{1.1},\quad C_{\text{yellow}}=\mathrm {e} ^{-2},\quad C_{\text{blue}}=-\mathrm {e} ^{-3/2},円}