In Problems 1–10 use the improved Euler’s method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.
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Chapter 9 Solutions
Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's ... Problems, 9th Edition, Single-Term
- Problem 3: Find the second derivative y of In Iny) + Inx= Iny. B X+Y C. D. in y y-x inx x-yarrow_forward0. A particle moves along the x-axis. The velocity of the particle at time t is given by v(t) = 4 If the %3D t+1 position of the particle is x 1 when t = 2, what is the position of the particle when t = 4 ? (A) 0.617 (B) 0.647 (C) 1.353 (D) 5.713arrow_forwardQuestion 20arrow_forward
- Full solution is required. Problem 2. Let f(x) = g(x? + 1), where g'(2) = 3 and g"(2) = 5. Compute f"(1). Full solution is required. %3Darrow_forwardCan you solve this using "A=5, B=0"?arrow_forward3. Use Euler's method to approximate the value of = -2x3 + 12x2 - 20x + 8.5 from x = 0 to x = 4. The initial condition is y(0) = 1. Use the following step size: a. h= 0.5 dx b. h 0.25 C. h 0.1 d. Compute for the true error and relative percentage error using the true value of y = -0.5x* + 4x3 + 8.5x + 1 at x-4 for each given steps. 1. Ka Ping has decided to save money roughly P100 per week. Suppose he makes a bi-monthly deposits of this money into a bank account that pays annual interest of 10%, compounded continuously. Use annuity formula: = rS + d; S(0) = So ds %3D dt a. Use Euler's method and approximate the balance after 4 years. b. Solve the general solution of the given annuity formula and solve for the exact value. 3 dy 2. 32+5y = sin x, y(0.3)= 5 and using a step size of h = 0.3, Approximate the value of y(0.9) dx using Euler's method.arrow_forward
- Example 10.15. Apply Runge-Kutta fourth order method to find an approximate value ofy when x = 0.2 given that dy/dx = x +y and y = 1 when x = 0.arrow_forwardProblem 1.6.12. (Implicit Differentiation). You know how to find the derivative dy/dx when y(x) is given. Suppose instead I tell you that y and x are related by an equation, say x2 + y² = R² and ask you to find the derivative at each point. There are two ways. The first is to solve for y as a function of x and then let your spinal column take over, i.e., by changing x infinitesimally and computing the corresponding change in y given by the functional relation. The second is to imagine changing x and y infinitesimally while preserving the constraining relation (a circle in our example). The latter condition allows us to relate the infinitesimals Ar and Ay and allows us to compute their ratio in the usual limit. Show that the derivative computed this way agrees with the first method. Find the slope at the point (2, 3) on the ellipse 3x2 + 4y2 = 48 using implicit differentiation. %3D %3Darrow_forward1.arrow_forward
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