374: 1.4 Examples
374: 1.4 Examples
Example 4
Example 4
Plot some examples of the family of solutions of the first order ODE =+1.
dy
dx
3
2
x
Plot[{3ArcTan[x]+3,3ArcTan[x]+1,3ArcTan[x],3ArcTan[x]-1},{x,-π,π}]
Example 5
Example 5
Given that solutions of the second order ODE are of the form , sketch some solutions.
y''+y=0
y=cosx+sinx
c
1
c
2
Plot[{Cos[x]+Sin[x],Sin[x],-4Sin[x]},{x,0,2π}]
Example 6
Example 6
Sketch a few members of the one-parameter family of curves given by (9), +=:
2
(x-a)
2
y
2
a
ContourPlot[{(x+1)^2+y^2(-1)^2,(x+2)^2+y^2(-2)^2,(x-1)^2+y^2(1)^2,(x-2)^2+y^2(2)^2},{x,-4,4},{y,-4,4},AxesTrue]
