(1 point) Suppose y2 y2 3 3 2 2 y(t) = cie + cze [1] 1 y1 y1 [-1] 7(1) = [21] -3 -2 2 3 -3 -2 -1 1 2 3 -1 -2 -3 -3 (a) Find ci and C2 А B C1 = 1.3591 y2 y2 3 3 C2 = 0.1839 2 2 1 1 y1 y1 -2 -1 1 2 3 -3 -2 -1 1 2 3 (b) Sketch the phase plane trajectory that satisfies the given...
(3 points) Suppose 30 = creº [!]+cze [1] 70 = [13] (a) Find ci and C2. C1 = C2 = (b) Sketch the phase plane trajectory that satisfies the given initial condition. Which graph most closely resembles the graph you drew? Choose a (c) is the solution curve headed toward or away from the origin as t increases? A. toward B. away C. neither toward nor away
(1 point) Suppose 41 yl i(1) = (a) Find ci and c2 (b) Sketch the phase plane trajectory that satisfies the given initial condition. Which graph most closely resembles the graph you drew? B (c) What is the approximate direction of travel for the solution curve, as t increases from -oo to o0? OA. along the line y toward the origin and then along the line y-z away from the origin 41 yl B. along the line y z toward...
please help answer(b) and (c)
t least one of the answers above is NOT correct. (1 point) Suppose |巴 ¥ 当 3 2 (七) = Cie 1 1 ce [] vec[/I] (1) [] y1 1 -3 -1 2 - - =1 自 2 3 -1 -」 -2 =2 A B 9 2 2 (b) Sketch the phase plane trajectory that satisfies the given initial condition. Which graph most closely resembles the graph you drew? B 1 1 y1 ul -...
(1 point) Suppose (a) Find cy and c2 (b) Sketch the phase plane trajectory that satisfies the given initial condition. Which graph most closely resembles the graph you drew? Choose (c) What is the approximate direction of travel for the solution curve, as t increases from -oo to -+o0? A. along the line y the origin z toward the origin and then along the line y z away from B. along the line y toward the origin and then along...
if y1(t) and y2(t) are two solutions of the differential equation y^2-y'+y=0 then for any constants c1 and c2 c1y1(t)+c2y2(t) is also a solution true or false and why
Question 2 (30 points) Integrate f(x, y,2) xzv2-z2 - y2 over the path C, which consists of two curves, C1 and C2 from (1, 0, 0) to (1,0, 0), then to (-1,3, 0). Curve C1 is only half of the circle2 Curve C2 is a straight-line segment. The parametric equation for G is G: r! (t)-cos t î + sin t k, 0 π Find the line integral: Jcf(x. y,z)ds - (25 points) C2 (-1,3,0)
Question 2 (30 points) Integrate...
If y is a known nonvanishing solution of y" p(t)y + q(t)y 0, then a second solution y2 satisfies 2 У1? where W(y1, y2) is the Wronskian of y1 and y2. To determine y2, use Abel's formula, W(y1, Y2)(t) =C.eJP(t) dt, where C is certain constant that depends on y1 and y2, but not on t. Use the method above o find a second independent solution of the given equation. (х — 1)у" - ху" + у %3D 0, x>...
2. Use Definition to find the equation of the tangent line to the graph of the equation y- 1/2 at -2 3. Find the points on the graph of y2-/2 at which the tangent line is parallel to the line y - 3. 4. Sketch the graph of a continuous function f that satisfies all of the stated conditions. f(0) 2, f(-2)- (2)-0, f(-2) f(O)-f'(2)-0 f"(z) > o if-2<zco, f,(z) < 0 if <-2 or x > 0;
2. Use...
Please solve these three questions!
(1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C1 function g : [a, b - IR. Show that the path integral of a continuous function f: IR2- R over the path C is b) Let g : [a, b] - IR be a piecewise C1 function. The length of the graph of g on (t, g(t)). Show that [a,b]...