Find that solution of the system such that yı(0) = 1, 42(0) = 1. y1 =...
5. Consider the system of differential equations yi = y1 + 2y2, y = -41/2 + y2 with initial conditions yi(0) = 1, y2(0= 0. This has exact solution yı(t) = exp(t) cos(t), yz(t) = - exp(t) sin(t)/2. (a) Apply Euler's method with h=1/4 and find the global truncation error by comparing with the exact solution over the interval [0, 1]. (b) Apply the RK4 method with h=1 and find the global truncation error by comparing with the exact solution...
Given that yı(x) = r-1 is a solution of 2c?y" + 3ry - y=0. Find a second solution of the given equation by using the method of reduction of order. O y2(:-) = O 42(:) = 1-1/2 O 42(x)=1/2 O y2(x) = 73/2 Oy2(r) =
Q 3. The joint density of Yı, Y2 is given by e-4342 p(y1, y2) = - T, Y1 = 0,1, 2, ...; Y2 = 0, 1, 2, ... a. Find the marginal distribution of Yı. b. Find the conditional distribution of Y2 given that Y1 = yı. c. Determine if Yı and Y2 are independent - justify; you can use your result from b.
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
The indicated function yı() is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, Y2 = vy() / e-SP(x) dx dx (5) y?(x) as instructed, to find a second solution y2(x). x?y" + 2xy' – 6y = 0; Y1 = x2 Y2 The indicated function yı(x) is a solution of the given differential equation. 6y" + y' - y = 0; Y1 Fet/3 Use reduction of order or formula (5) in Section...
find Y1=, Y2=, and W(t)=
(1 point) Find the function yi of t which is the solution of 25y" – 40y' + 12y = 0 y(0) = 1, yf(0) = 0. with initial conditions Yi = Find the function y2 of t which is the solution of 25y" – 40y' + 12y = 0 with initial conditions Y2 = Find the Wronskian W(t) = W(y1, y2). W(t) = Remark: You can find W by direct computation and use Abel's theorem...
Chapter 4, Section 4.7, QUestion 23 Given that the given functions yı and y2 satisfy the corresponding homogeneous equation; find a particular solution of the given nonhomogeneous equation ty (3t1y +3y = 8172e6 > 0; y1 (t) = 3t , y2 (t) = e3 The particular solution is Y(t) =
Chapter 4, Section 4.7, QUestion 23 Given that the given functions yı and y2 satisfy the corresponding homogeneous equation; find a particular solution of the given nonhomogeneous equation ty (3t1y...
Two linearly independent solutions of the differential y" - 4y' + 5y = 0 equation are Select the correct answer. 7 Oa yı = e-*cos(2x), Y1 = e-*sin(2x) Ob. Y1 = et, y2 = ex Oc. yı = e cos(2x), y2 = e* sin(2x) Od. yı=e2*cosx, y2 = e2*sinx Oe. y = e-*, y2 = e-S*
Two solutions to y' + 6y + 25 = 0 are y1 = = e 3t sin(4t), y2 = e cos( 4t). a) Find the Wronskian. W b) Find the solution satisfying the initial conditions y(0) = - 4, y'(0) = 0 y =
17. Another way to check if y1, y2 are linearly INDEPENDENT in
an interval I is:
for all I
for all I
does not exist for all I
d. none of the above
18. If y1 is a solution of the equation y "+ P (x) y '+ Q (x) y
= 0, a second solution would be y2 (x) = u (x) y1 (x) where u (x)
it is:
d. all of the above
19. The following set...