23. The slope field for a differential equation f(x,y) is given in the figure. The slope...
81. A slope field for a differential equation is shown in the figure above. If \(y=f(x)\) is the particular solution to the differential equation through the point \((-1,2)\) and \(h(x)=3 x \cdot f(x)\), then \(h^{\prime}(-1)=\)(A) \(-6\)(B) \(-2\)(C) 0(D) 1(E) 12
1. Consider the differential equation y' = y-t. (a) Construct a slope field for this equation. (b) Find the general solution to this differential equation. (c) There is exactly one solution that is given by a straight line. Write the equation for this line and draw it on the slope field.
4. (4 pts) The slope-field of a differential equation is given. Let y(x) be the solution with initial condition y(0) = 1.7. Estimate the minimum point of v(x). Give estimates of both coordinates r and y of the minimum point.
The slope field for the equation dy/dx = x+y for −4 ≤ x ≤ 4, −4 ≤ y ≤ 4 is shown in the figure below. The slope field for the equation yxy for -4 SxS4, -4 Sy s4 is shown in the figure below TA (a) Sketch the solutions that pass through the following points: -Select The solution has slope at (0, 0) and is Concave up concave down inear (ü) (-3, 1)increasing The solution sdecreasing -Select concave up...
Consider the differential equation dy/dx = (y-1)/x. (a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. (b) Let y = f (x) be the particular solution to the given differential equation with the initial condition f (3) = 2. Write an equation for the line tangent to the graph of y= f (x) at x = 3. Use the equation to approximate the value of f (3.3). (c) Find the particular solution y...
dy The slope field below is that for some differential equation = f(t, y) 1 1 1 1 1 2 From this, give a possible solution to the differential equation y 42-1-\3A.
Consider the differential equations The slope field depicted below corresponds to one of these Which differential equation matches the direction field?
C Consider a differential equation with the given slope field and the in y(0) = 1. 0.5 st -0.5 (a) Explain why, if you wanted to approximate y(2) using two steps of Euler's method, you would need At = 1. (b) Use a straight edge to graph two steps of Euler's method to approximate y(2). (c) This time, instead of using two steps of Euler's method, sketch on the same slope field what it would look like if you used...
32 111 8. Shown above is a slope field for the differential equation d dy 2 4 v2 If y - g(r) is the solution to the differential equation with the initial condition g(-12 ,then lim slx) =-1, then lim g(x) is (B) -2 (C) 0 (D) 2 (E) 3 32 111 8. Shown above is a slope field for the differential equation d dy 2 4 v2 If y - g(r) is the solution to the differential equation with...
The slope field for the equation y'=-x+y is shown above On a print out of this slope field, sketch the solutions that pass through the points (i) (0,0); (ii) (-3,1); and (iii) (-1,0). From your sketch, what is the equation of the solution to the differential equation that passes through (-1,0)? (Verify that your solution is correct by substituting it into the differential equation.)