MediumFirst-order

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.5 Separable Equations Including the Logistic Equation, #22 · Differential Equations · First-order

To solve … change to

To solve $y^{'} = cy - b y^{3}$ change to $u = 1/ y^{2}$ . Substitute for $y^{'}$ in $u^{'} = - 2 y^{'} / y^{3}$ to find a linear equation for $u$ . Solve it as in (14) but with $u_{0} = 1/ y_{0}^{2}$ . Then $y = 1/ u$ .

~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, #22

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.