Differential Equations: Separation of Variables - Exercises and Examples, Slides of Differential Equations

with a slope of 8 at the point (4, 11): d2y/dx2 = ¾x. 6.2--Differential Equations. The birth of the Pert formula!!! dy/dt = ky. (direct variation). A = Pert.

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1) Find the function y = f(x) having the given 2nd derivative
with a slope of 8 at the point (4, 11):
d2y/dx2 = ¾x
6.2--Differential Equations
The birth of the Pert formula!!!
dy/dt = ky
(direct variation)
A = Pert a.k.a. y = Cekt
pf3
pf4
pf5

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1) Find the function y = f(x) having the given 2nd derivative

with a slope of 8 at the point (4, 11):

d^2 y/dx^2 = ¾ x

6.2--Differential Equations

The birth of the Pe

rt

formula!!!

dy/dt = ky (direct variation)

A = Pe

rt

a.k.a. y = Ce

kt

6.3--Separation of Variables Find the general solution for each differential equation: textbook # 5 : dr/ds = .75r textbook #6: dr/ds = .75s

6.3--Separation of Variables Textbook #26: Find the equation of the graph that passes through (1,1) & has the given slope: y' = -9x 16y Notice they said "graph", not "line".

6.3--Separation of Variables

  1. dy/dx = 6y - 4x Let y = f(x) be a particular solution to the differential equation with the initial condition f( 9 ) = 6. Does f have a relative minimum, a relative maximum, or neither at x = 9? Justify your answer.