What is the solution for P^'=(P)(t)(1-P/(10)) ?

The solution for P^'=(P)(t)(1-P/(10)) is P(t)=-(10e^{(t^2)/2+c_{1}})/(1-e^{(t^2)/2+c_{1)}}

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P^'=(P)(t)(1-P/(10))

P^{^{'}} = (P) (t) (1 - \frac{P}{10})

P (t) = - \frac{10 e ^{\frac{t ^{2}}{2} + c_{1}}}{1 - e ^{\frac{t ^{2}}{2} + c_{1}}}

Solution steps

P^{'} (t) = (P (t)) (t) (1 - \frac{P ( t )}{10})

Solve separable ODE:

P (t) = - \frac{10 e ^{\frac{t ^{2}}{2} + c_{1}}}{1 - e ^{\frac{t ^{2}}{2} + c_{1}}}

P (t) = - \frac{10 e ^{\frac{t ^{2}}{2} + c_{1}}}{1 - e ^{\frac{t ^{2}}{2} + c_{1}}}

What is the solution for P^'=(P)(t)(1-P/(10)) ?
The solution for P^'=(P)(t)(1-P/(10)) is P(t)=-(10e^{(t^2)/2+c_{1}})/(1-e^{(t^2)/2+c_{1)}}