Show that the one-parameter family satisfies the differential equation for all real

MATHEMATICS · Subjective · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

Show that the one-parameter family

y=\dfrac{1}{1+Ce^{-x}}

satisfies the differential equation

\dfrac{dy}{dx}=y\,(1-y)

for all real

x

. Then determine the value of

C

that yields the solution satisfying

y(0)=\tfrac14