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EBK DIFFERENTIAL EQUATIONS AND LINEAR A
- 1. Solve the following first-order equation: (2ry + 3y?)dr - (2xy+x?)dy = 0.arrow_forwardPlease provide me with the answer and solution. Please dumb it down so I can understand.arrow_forwardAn amusement park has two ferris wheels that both load passengers at the bottom, 3 m above the ground. Both wheels require 40 seconds to complete one revolution. The larger ferris wheel has a diameter of 25 m and the smaller ferris wheel has a diameter of 10 m. The height of a passenger on each wheel can be expressed in the form h(t) = a cos[b(tc)] + d, where h(t) is the height above the ground in metres t seconds after the ride begins. 25 m 3m 14 O a and b O a and d TOT Ob and c Oc and d 10 m 3 m A 76 If the ferris wheels have the same period of rotation, then the two parameters that must be the same in the two functions are Groundarrow_forward
- Classify each of the following equations as linear or nonlinear (explain you're the reason). If the equation is linear, determine further whether it is homogeneous or nonhomogeneous. a. (cosx)y"-siny'+(sinx)y-cos x=0 b. 8ty"-6t²y'+4ty-3t²-0 c. sin(x²)y"-(cosx)y'+x²y = y'-3 d. y"+5xy'-3y = cosy 2. Verify using the principle of Superposition that the following pairs of functions y₁(x) and y2(x) are solutions to the corresponding differential equation. a. e-2x and e-3x y" + 5y' +6y=0 3. Determine whether the following pairs of functions are linearly dependent or linearly independent. a. fi(x) = ex and f(x) = 3e³x b. fi(x) ex and f2 (x) = 3e* 4. If y(x)=e³x and y2(x)=xe³x are solutions to y" - 6y' +9y = 0, what is the general solution? Question 1. Classify each of the following equations as linear or nonlinear (explain you're the reason). If the equation is linear, determine further whether it is homogeneous or nonhomogeneous. a. (cosx)y"-siny'+(sinx)y-cos…arrow_forwardShow that the equation y'' + y = 0 is satisfied for y = πsinθ + 2πcosθarrow_forwardA bungee jumper dives from a tower at time t = 0. Her height h (measured in feet) at time t (in seconds) is given by the graph on the 2nd page. In this problem, you may base your answers on estimates from the graph or use the fact that the jumper's height function is given by s(t)= 75 cos (0.9x) · e-0.3x + 60. If you would like to view the graph on Desmos, you will find it here: https://www.desmos.com/calculator/yozi9dijkd 1. What is the change in vertical position of the bungee jumper between t = 0 and t = 16? You may estimate using the graph or use the function. If you use the function, round to 1 decimal place. In either case, be sure to show all work as to how you arrived at the solution. 2. Estimate the jumper's average velocity on each of the following time intervals: [0,16] and [3,6]. Include the units and appropriate positive/negative sign.arrow_forward
- Example 2.34. Apply Muller's method to find the root of the equation cos x = xe which lies between 0 and 1.arrow_forwarda. Show that g(t) = sin2 t - 3t decreases on every interval in its domain. b. How many solutions does the equation sin2 t - 3t = 5 have? Give reasons for your answer.arrow_forwardfor a fixed location, the number of sunlight hours in a day fluctuates throughout the year. Suppose that the number of daily sunlight hours in a particular ocation can be modeled by the following. L()12+3.6 cos 365 In this equation, L() is the number of sunlight hours in a day, and f is the number of days after June 218. (So t-0 means June 21s, t-1 means June 22nd 1-2 means June 23rd, etc.) Suppose we start at -0, which is June 218 During the first 365 days, when will there be 11 hours of sunlight? Do not round any intermediate computations, and round your answer(s) to the nearest day. (If there is more than one answer, enter additional answers with the "or" button.) days after June 21" Explanation Check 72022 MrGraw Hill LLC AR Rignts Reserved Terms of Use nyacy Center Accesbilty 19 tv 80 F2 F3 DII DD F4 FS F6 F8 F9 F19arrow_forward
- Solve the equation cos (20) = sin(0), for 0 € [0, 27]arrow_forward4. Find the a. y = x² sin x b. y = ex cos x 3 c. y = (x² + 1)^¹ (²-1) ²³ 2x+1 d. y = e. y = derivative of the following functions: x²-4 5x+1 2√√x-1arrow_forwardNear the grounds of a building is a windmill h(t)=2 cos (30t)+6, where h(t) is the height of the blade above the ground and t is the time in seconds. If the rotation begins at the blade with the highest possible height, at what time(s) will the blade be exactly 7.8m above the ground within the second rotation?arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage