## Qualitative solution sketching for first order differential equations |

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asymptote brium solution calculate called logistic capita rate Census classified as stable Consider constant of integration constant of proportionality correct concavity correct slope curves are horizontal Difficult Example direction field ential equation equi Equilibrium solutions Exercise 22 Exercises 1-19 exhibit approximately exhibit the correct family of solutions Find the differential graph solutions graphically Hence all solution horizontal solution horizontal translates ibrium points Idento-KIt iqht island jiggle Look negative number line number of bacteria number of solutions number of species nutrients order differential equation partial fractions piece point x,y points and classify points of inflection problem proper slope QUALITATIVE SOLUTION SKETCHING rate of growth rate proportional Relevance of Uniqueness second derivative Sketch a number Sketch solutions sketch some solutions Sketch the curve sketches should exhibit slope and concavity slopes get steeper slopes occur solu solution curves Solve the differential stable equili stable or unstable sure your curve tion uniqueness theorem applies