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Chapter 1: Q16RP (page 30)

Using the method of isoclines sketch the direction field for\[{\bf{y = - }}\frac{{{\bf{4x}}}}{{\bf{y}}}\].

Short Answer

Expert verified

The graph is drawn below.

Step by step solution

01

The isoclines curve

Here the isoclines curve is

\[\begin{array}{c}\frac{{{\bf{ - 4x}}}}{{\bf{y}}}{\bf{ = c}}\\{\bf{y = }}\frac{{{\bf{ - 4x}}}}{{\bf{c}}}\end{array}\]

By putting the values of c we the graph.

By putting the different values of c=1,-1,2,-2 get the graph.

02

Slope field

By using the software we get the slope field.

By using the software and putting the different values of x get the slope field.

03

Direction field

By using the software get the direction field.

By using the software and putting the different value get the direction field.

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Most popular questions from this chapter

In Problems 23-28, determine whether Theorem 1 implies that the given initial value problem has a unique solution.

ydydx=x,y(1)=0

In Problems 10–13, use the vectorized Euler method with h = 0.25 to find an approximation for the solution to the given initial value problem on the specified interval.

(1+t2)y''+y'-y=0;y(0)=1,y'(0)=-1on[0,1]

Use Euler’s method with step size h = 0.1 to approximate the solution to the initial value problem

y'=x-y2, y (1) = 0 at the points x=1.1,1.2,1.3,1.4and1.5.

Consider the differential equation dydx=x+siny

⦁ A solution curve passes through the point (1,π2). What is its slope at this point?

⦁ Argue that every solution curve is increasing for x>1.

⦁ Show that the second derivative of every solution satisfies d2ydx2=1+xcosy+12sin2y.

⦁ A solution curve passes through (0,0). Prove that this curve has a relative minimum at (0,0).

Question:Use a CAS to graphJ3/2(x),J-3/2(x),J5/2(x), and J-5/2(x).
See all solutions

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