Solução_Calculo_Stewart_6e

F.
384 ¤ CHAPTER 9 DIFFERENTIAL EQUATIONS
TX.10
15. In Maple, we can use either directionfield (in Maple’s share library) or
DEtools[DEplot] to plot the direction field. To plot the solution, we can
either use the initial-value option in directionfield, or actually solve the
equation.
In Mathematica, we use PlotVectorField for the direction field, and the
Plot[Evaluate[...]] construction to plot the solution, which is
y = 2 arctan e x3 /3 · tan 1 .
2
In Derive, use Direction_Field (in utility file ODE_APPR) to plot the direction field. Then use
DSOLVE1(-xˆ2*SIN(y),1,x,y,0,1) (in utility file ODE1) to solve the equation. Simplify each result.
17. The direction field is for the differential equation y 0 = y 3 − 4y.
L = lim
t→∞
y(t) exists for −2 ≤ c ≤ 2;
L = ±2 for c = ±2 and L =0for −2