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In Problems 1–8 use the method of undetermined coefficients to solve the given nonhomogeneous system.
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Chapter 8 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
- 1. Use RK4-Systeml to solve each of the following for 0sIs1.Use h = 2-k with k = 5, 6, and 7, and compare results. (x" =x² - y +e x" = 2(e - x)/2 y" = x - y -e b. %3D a. x(0) = 0 x'(0) = 1 x (0) = 0 x'(0) = 0 y(0) = 1 y'(0) = -2arrow_forwardProblem 2. Consider the equation: x?y"(x) – xy' +y = 0. Given that yı(x) = x is a solution of this equation. Use the method of reduction of order, find the second solution y2(x) of the equation so that y1 and y2 are linearly independent. (Hint: y2(x) should be given in the form y2(x) = u(x)y1(x). Substitute it into the equation to find u(x).) %3Darrow_forward1. Suppose we are given y1(x) and y2(x) (with y1 ≠ y2), which are two different solutions of a nonhomogeneous equation y′′+p(x)y′+q(x)y=g(x)(1)In three steps, describe how to write down the general solution of (1): Step 1: Step 2: Step 3:arrow_forward
- #14arrow_forwardQ. No. 11 The solution of the DE 3ry" + y/ – y = 0 (a) yı = rš[1 – {x +²+...], y2 = 1+x – 20² + ... (b) yı = a3[1 – r +a² + ...], y2 = 1+ 2x – 2x² + ... (c) yı = xš[1 – x + a² + ...], y2 =1+ 2x – 2x3 + ... (d) yı = [1 – x + x² + ...], y2 = 1+ 2x – 2x2 +... solve this and tick the correct optionarrow_forward14. If ey = 3x² and y(1) = 2, then the particular solution y(x) is A. y = In x³ + 2 B. y = 2e*³-1 C. y = In (x³ + e² – 1) D. y = x³ + e² –1arrow_forward
- 16arrow_forwardIf the given solutions 2 – 2t yi(t): y2(t) = 2t form a fundamental set (i.e., linearly independent set) of solutions for the initial value problem 21-2 1– 21-1 + 21-2 -23 y, y(3) = t > 0, y -2t-2 2t-1 – 21-2 -34 impose the given initial condition and find the unique solution to the initial value problem for t > 0. If the given solutions do not form a fundamental set, enter NONE in all of the answer blanks. 2t 0) = At) = ( + ( 2tarrow_forward8.3 I only need number 14 pleasearrow_forward
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