Instructions for forms of answers in differential equation problems For second order DEs, the roots of...
(15 points) This problem is related to Problems 7.5-7.8 in the text. Given the differential equation y' + 5y = 9cos(5t + 0.523599)u(t). Remember to use u(t) in Webwork answers when the solution is for t > 0. For differential equations, angles are given in radians. a. Find the complementary solution, yc(t), with constants denoted C1, C2, ... yc(t) = help (formulas) b. Find the particular solution, yp(t). yp(t) = help (formulas) c. Find the total solution, y(t) for the...
All numerical angles(phases) should be given in radian angles (not degrees). Given the differential equation y" +12y' +45y - 6u(t) a. Write the functional form of the complementary solution, ye(t). e(t) help (formulas) b. Find the particular solution, yp(t). help (formulas) c. Find the total solution, y(t) for the initial conditions y(0)-8 and y'(0) 10 y(t) help (formulas) All numerical angles(phases) should be given in radian angles (not degrees). Given the differential equation y" +12y' +45y - 6u(t) a. Write...
Consider the differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation above. T1,T2 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. n(t) = v2(t) (c) Find a particular solution yp of the differential equation above. Bplt)
Consider the following differential equation: 4y(4) + y" - 18y' + 13y = et a) Knowing that r1 = 1 is a double root, find the other two roots. b) Find the corresponding complementary solution yc(t). c) Find the corresponding particular solution yp(t).
(1 point) a. Find a particular solution to the nonhomogeneous differential equation y" + 3y - 10y = ex. yp = help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use cy and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2. Yh = help (formulas) c. Find the most general solution to the original nonhomogeneous differential equation. Use cy and C2 in your answer to denote arbitrary constants....
Previous Problem Problem List Next Problem (10 points) This problem is related to Problems 9.33-9.38 in the text. We have solved differential equations using the method of undetermined coefficients (Chapter 7) and Laplace transforms (Chapter 8). We can use Fourier series to find the particular solution of an arbitrary order differential equation - as long as the driving function is periodic and can be represented by a Fourier series In the problem description and answers, all numerical angles(phases) should be...
Consider the differential equation y" – 7 ý + 12 y = 3 e21. (a) Find r1, r2, roots of the characteristic polynomial of the equation above. W r1, r2 = 3,4 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) = e^(3t) M y2(t) = e^(41) (c) Find a particular solution Yp of the differential equation above. M yp(t) = Note: You can earn partial credit on this problem.
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" +9y sec(3x) a. Find the most general solution to the associated homogeneous differential equation. Use c1 and c2 in your answer to denote arbitrary constants, and enter them as ct and c2. help (formulas) b. Find a particular solution to the nonhomogeneous differential equation y" +9y sec(3x). yp elp (formulaS c. Find the most general solution to the original nonhomogeneous differential equation. Use c...
Find the second order linear differential equation whose general solution is given by y=C1 cos4t + C2 sin4t -e^t sint
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2, roots of the characteristic polynomial of the equation above. 11,12 M (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) M y2(t) = M (C) Find the Wronskian of the fundamental solutions you found in part (b). W(t) M (d) Use the fundamental solutions you found in (b) to find functions ui and Usuch...