What is the solution for (dr)/(ds)=e^{r+s},r(1)=0 ?

The solution for (dr)/(ds)=e^{r+s},r(1)=0 is r=-ln(-e^s+1+e)

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(dr)/(ds)=e^{r+s},r(1)=0

\frac{d r}{d s} = e^{r + s}, r (1) = 0

r = - ln (- e^{s} + 1 + e)

Solution steps

\frac{d r}{d s} = e^{r + s}

Solve separable ODE:

r = - ln (- e^{s} + 1 + e)

r = - ln (- e^{s} + 1 + e)

\frac{d p}{d t} = k p (t) ln (\frac{4.5}{p})

y^{^{'}} = (x + 2) y

\frac{d y}{d x} = 4 y x, y (1) = 6

(1 - x^{2}) y^{^{'}} - 2 y = 0

x = - 0.014985 \frac{d x}{d t}

What is the solution for (dr)/(ds)=e^{r+s},r(1)=0 ?
The solution for (dr)/(ds)=e^{r+s},r(1)=0 is r=-ln(-e^s+1+e)