please do do 1 a,b,c,d,e and 2 a, b Text exercise 26 Determine where each of...
IV. Determine the form for yp but do NOT evaluate the constants. 1. y" - 5y' + 6y = ex cos 2x + e2x(3x + 4) sin x (ans. this is #21(a) in sec. 3.6) 2. y" - 3 y' - 4 y = 3 e2x + 2 sin x - 8eXcos 2x (ans. Yp = Ae2x + B cos x + C sin x + De* cos 2x + E e sin 2x) V. Solve by variation of parameters....
7. Identify each ODE type HG, Bernoulli, or Neither and write the correct u-substitution (DO NOT SOLVE) for solving the ODE. a) y' (3 + 4x) = 4y(x - 2y) b) (x2 - y2)y' = x - y32 - y2 c) xy' = (x – y)cos? d) 4yy' - 3x = ye -2x/y
Please only fill in the red blanks (2 points) is typed as lambda, a as alpha. The PDE yº au au ar ay is separable, so we look for solutions of the form u(x, t) = X(2)Y(y). When solving DE in X and Y use the constants a and b for X and c for Y. The PDE can be rewritten using this solution as (placing constants in the DE for Y) into X"/X = (1/(k^2))(y^5)(Y'/Y) -2 Note: Use the...
1. Starting with the equation a tanh y show that, for real r, y and |rl < 1, y-tanh-1 2. Compute the following derivative dtanh (sin() 3. Assume θ is a real number. Then use Euler's formula eie-cos θ + isin θ to show that coth(i0)-icot(e) 4. Use the definitions to obtain an equation for cosh(3x) in terms of cosh(x) and sinh(x) and their various products (e.g., cosh*(z), cosh(x) sinh3(x) etc.). Do not use the double-angle formula such as cosh(u+...
Please answer number 2 & not number 1 Ln(x) e = x Exercises VI 1. (Bonus) Prova 2. Find the general solution. z = 7? COS (*) = 2ze (a) y + 4y (b) y + sin(x) y dy + xy dx (d) dy + 2y (e) dx (c) 2 χ 8x² cos? (x) dx ت = ay dy sin (3x) dx - Х dy = Ln(y) dy
5. Evaluate the following differentials (a) det? (b) d sinh ở (c) dx sin (d) do y 6. Find the exact values of the following expressions. Justify your answers using the definitions of they hyperbolic functions. (a) sinh (In 3) (b) cosh (In 3) (c) tanh (In 3) 7. Suppose cos 2 + siny = 1 (a) Use implicit differentiation to find y' = dy. Simplify your answer as appropriate. (b) Use implicit differentiation to find y" dy. Simplify your...
(1 point) х Suppose w 9 y + where у 2 + sin(2t), and z = z X = e e5t, y 2 + cos(7t). as X. dw A) Use the chain rule to find as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e e5t d dw 5/y(e^5t)+-x/y^2+1/z(2cos(2t))+(-y/3^2)*(-7sin(7t)) dt Note: You may want to use exp() for the exponential function. Your answer should be...
#32 U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In Problems 31-36, determine the form of a particular solution for the differential equation. Do not solve. 31. y" + y = sin : + i cos + + 10' 32. y" - y = 2+ + te? + 1221 x" - x' - 2x = e' cos - + cost y" + 5y' + 6y = sin t - cos 2t 35. y" –...
<---- equation (6) Using the equation (6) in page 569 of our text, obtain the solution of ut-CUx -lx in integral form satisfying the initial condition u(x, 0) = e- 30 1 | [A(p) cos px + B(p)sin px) e-c2p2tdp 11 (x, t; p) dp= u(x, t)= 0 Using the equation (6) in page 569 of our text, obtain the solution of ut-CUx -lx in integral form satisfying the initial condition u(x, 0) = e- 30 1 | [A(p) cos...
Please do b and d. The result for 26.5 a is below 26.6. Using the results from exercise 26.5 a, find the solution to y" + 4y fo with y(0) = 0 and y'(0) = 0 for each of the following choices of /: a. fo = 1 b. - 1 d. f(1) = sin(21) e. f(1) = sin(a) where a #2 c. / (0) = 1 26.5 a. C[SOL {[y" + 4y]. [Y'). + 4L[y]1, → = F(s) [s?Y(s)...