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...
the simplest solution please fit for ap calculus ab l1T 8. Shown above is a slope ficld for the differential eoquaton is the solution to the y (4-y-]. If y - gx) is the solution to the differential equation with the initial condition g(-2)-1, then im g(x) is roo (A) -(B -2 (C)0 (D) 2 (E) 3 l1T 8. Shown above is a slope ficld for the differential eoquaton is the solution to the y (4-y-]. If y - gx)...
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
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.
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
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...
8. Solve the following differential equation given the initial condition y(0) = -5: dy 2.c dr 1+22 9. Solve the following differential equation using the method of separation of variables: dy = x²y. dic
1. Find the particular solution of the differential equation dydx+ycos(x)=2cos(x)dydx+ycos(x)=2cos(x) satisfying the initial condition y(0)=4y(0)=4. 2. Solve the following initial value problem: 8dydt+y=32t8dydt+y=32t with y(0)=6.y(0)=6. (1 point) Find the particular solution of the differential equation dy + y cos(x) = 2 cos(z) satisfying the initial condition y(0) = 4. Answer: y= 2+2e^(-sin(x)) Your answer should be a function of x. (1 point) Solve the following initial value problem: dy ty 8 at +y= 32t with y(0) = 6. (Find y as...
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...
Find the solution of the differential equation dy dx = x y that satisfies the initial condition y(0)=−7. Answer: y(x)=
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.)