MediumFirst-order

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.5 Separable Equations Including the Logistic Equation, #25 · Differential Equations · First-order

(c) This model is terrible because … goes to … as

A rumor spreads according to $y^{'} = y (N - y)$ . If $y$ people know, then $N - y$ don't know. The product $y (N - y)$ measures the number of meetings (to pass on the rumor).

(a) Solve $d y / d t = y (N - y)$ starting from $y_{0} = 1$ .

(b) At what time $T$ have $N /2$ people heard the rumor?

(c) This model is terrible because $T$ goes to $______$ as $N \to \infty$ . A better model is $y^{'} = b y (N - y)$ .

~8 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.5 Separable Equations Including the Logistic Equation, #25

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.