In Problems 1– 4 find the steady-state temperature u(r, θ) in a circular plate of radius r = 1 if the temperature on the circumference is as given.
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Chapter 13 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
- In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 3. x" + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375, x'(0) = 0arrow_forwardIn Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 4. x" + 25x = 90 cos 41; x (0) = 0, x'(0) = 90arrow_forward- Problem 5: A particle moves along a line with a velocity given by v(t) = t² – 2t where v is measured in meters per second. Find the displacement of the particle as well as the total distance traveled for 0 ≤t≤3.arrow_forward
- In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 2. x" + 4x = 5 sin 31; x(0) = x'(0) = 0arrow_forward2. Solve for y in terms of x for the following equations: a) In(1- 2y) = x %3D b) In(y - 1) - In 2 = x + In x c) In(y? - 1) – In(y + 1) = In(sin x) d) e(In 2)y 1/2arrow_forwardIf the length of a curve from (0,–3) to (3,3) is given by [ V1+(x² – 1)² dx , which of the following could be an equation for this curve? x (A) у%3 3 - 3 (В) у 3D -- 3x – 3 3 (С) у%3D—— х-3 3 (D) y =-+x- 3 3arrow_forward
- In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 5. mx" +kx = Fo cos wt with w # wo; x(0) = xo, x'(0) = 0arrow_forward1.11 Determine if the following equations are linear or nonlinear: a. y = 4 - 15x 3 b. y 3x X c. y = sin(2x + 4) d. y e. = 2x + 4- dy dt + 4y d²x = dt² dx dt 1/x +7 xdtarrow_forwardProblem 4. Find y as a function of x if a'y"- 5zy + 9y = x°, y(1) = -9, y (1) = 4. y =arrow_forward
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