In Problems 11–16 verify that the
16.
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
FIRST COURSE IN DIFF.EQ.-WEBASSIGN
- Problem 16 (#2.3.34).Let f(x) = ax +b, and g(x) = cx +d. Find a condition on the constants a, b, c, d such that f◦g=g◦f. Proof. By definition, f◦g(x) = a(cx +d) + b=acx +ad +b, and g◦f(x) = c(ax +b) + d=acx +bc +d. Setting the two equal, we see acx +ad +b=acx +bc +d ad +b=bc +d (a−1)d=(c−1)b That last step was merely added for aesthetic reasons.arrow_forward10. Determine three linearly independent solutions to the equation y" + 2y" – 3y = 0 of the form y(x) = e"*, where r is a real number. Remember to prove that these solutions are indeed linearly independent.arrow_forward7. Invert the following matrix 3x – 2y = 9 -x + 3y = 3 |arrow_forward
- 1. 2. 3. Write v as a linear combination of u and w, if possible, where u = (2, 3) and w = (1, -1). (Enter your answer in terms of u and w. If not possible, enter IMPOSSIBLE.) v = (-2, -3) V = Solve for w where u = (1, 0, -1, 1) and v = (2, 0, 3, -1). w + 2v = -4u W = Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, -1, 3), (5, 0, 4)) (a) z = (7, -6, 14). Z= (b) v = V = (c) w = (3,-9, 15) W = (d) v = (18, - 1, 59) )$₁ U= $₁ + u = (2, 1, -1) )$₁arrow_forward1. Solve for x and y in xy + 8 + j(x²y + y) = 4x + 4 + j(xy² + x) A. 2, 2, B. 2,3 C. 3, 2 2. Determine the principal value of (3 + j4)¹ +² +j2 A. 0.42+j0.56 C. -0.42-j0.66, B. 0.42+j0.66 D. 0.42-j0.66 3. Using the properties of complex numbers. determine the two square roots of 3-j2 A. +1.82+j0.55, C. 1.82 + j0.55 B. +1.82±j0.55 D. +1.82 + j0.55 4. Evaluate: BE CALC 3-14 3+14 + 3+j4 3-j4 A. 2.44 +j4/ B. 2.44-j4 C. -2.44 + j4 D. 2.44 +j5 Evaluate log; (3 + j4). A. 0.6+j1.02 C. -0.6-j1.02 B. -0.6+j1.02 D. 0.6-j1.02, 6. The following three vectors are given; A = 20 +j20, B = 30/120° and C= 10+ j0, find AB/C C. 95/-50° B. 85-75% A. 70/45° D. 75/70" 7. If 100+5x/45° = 200/-e. Find x and 8. A. 24. 23.28 B. 23.28. 32.3° C. 23.28. 24.3% D. 23, 42.8° 8. Determine the principal value of cosh' (j0.5). A. In (1+j5) C. In j5 B. In (1± √5), D. In j(1 + √5) 2 5 1 = 9. In A-2B-C=0. if A= 2B-C-0. if A- and B-₁ find C |² -1 3 2 3 8 -3 8 3 91 C. A. 3 0 0 -3 -8 -8 -3 3 D. B. | 3 0 -3 10. Solve for a and b…arrow_forwardThis is the first part of a two-part problem. Let O 21 P = -2 sin(2t)] -2 cos(2t)]* cos(2t) y1(t) sin(2t)| ÿ2(t) = a. Show that 1(t) is a solution to the system i' = Pý by evaluating derivatives and the matrix product O 2] -2 Enter your answers in terms of the variable t. b. Show that y2(t) is a solution to the system i' = Pj by evaluating derivatives and the matrix product %(t) y2(t) Enter your answers in terms of the variable t.arrow_forward
- This is the first part of a two-part problem. Let P=[-: 1 5₁(t) = [(41) 5₂(t) = - sin(4t). a. Show that y₁ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product y(t) = = 0 [1] -4 Enter your answers in terms of the variable t. -4 sin(4t) -4 cos(4t)] ÿ₁ (t) [181-18] b. Show that y₂ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product Enter your answers in terms of the variable t. 04] 32(t) = [-28]|2(t) 181-181arrow_forward2) 3 3 dr+du+ +y=t dr subject to x = 1 and y = 0 at t = 0arrow_forward11.3 11.4: Problem 7 Find the linearization L(x, y, z) of the f(x, y, z) = 2/ x³ + y³ + z³ at the point (1, 2, 3). Answer: L(x, Y, z) =||arrow_forward
- of the form y₁ = (1+₁+ a₂²+az³ + ...) 3₂ = x2(1+b₁x + b₂x² + b₂x³ + ...) where T₁ > T2- Enter Find two linearly independent solutions of 2x²y" - xy + (2x+1)y=0, z>0 T1 1 01 = a₂= 03 = T2= 1/2 b₁ = b₂ = b3 =arrow_forward7. Find two linearly independent solutions of y" + 3ay = 0 of the form y₁=1+ a32³ +as+... 32=2+b₁¹+b727 +.... Enter the first few coefficients: as 11 ag= b₁ == 41 (numbers) (numbers) (numbers) ›(numbers)arrow_forwardA If = + ƒ [_(x + 1) dx π = (x+2)(x-1)² x + 2 12 (A 9 3 B 9 O D 9 9 2 3 2 3 2 3 B x-1 + C (x-1)² dx, the values of A & C respectively are:arrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education