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In Problems 1–8 use the method of undetermined coefficients to solve the given nonhomogeneous system.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 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_forward3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c (х — у)"(х + у) %3 с (х + 2y) (2х- у)* %3 с (x – 2y)* = c(2x + y)arrow_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_forward
- 5.2. Solve the problem 0 0 Uzz = 0 u (x,0) = uz (r, 0) = 0 uz (0, t) = 1, u (1, t) 0 Utt %3! %3D t2 0.arrow_forwardExample 1. Show that the solutions of the following system of differential equations remain bounded as t 00: -uarrow_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
- Use (1) in Section 8.4 X = eAtc (1) to find the general solution of the given system. 1 X' = 0. X(t) =arrow_forward6. (2x +3y = 0 /2x x+2y =-1 9. (1 1 -X+-y 5 1, -x+y%3D10 4arrow_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: 2.Find the general solution of y′′+y= sec(x)arrow_forward
- Q. 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_forwardIn Problems 1–8 use the method of undetermined coeffi cients to solve the given system. dx 1. = 2x + 3y – 7 dt dy 2у + 5 = -x - dt dx 2. dt 5х + 9у + 2 dy — —х + 11у +6 dt -G )x+ (,) 3 3. X' = 3 t (4t + 9er\ 4. X' = 4 -4 х+ 1 -t + e6t 3 X + le' 10 5. X' = sin t 5 X + 1 6. X' 1 -2 cos 7. X' = 2 3 X +| -1 \0 0 5, 2 8. X' = 5 0 ]X + - 10 5 0 0/ 40/arrow_forward1. Consider the accidental death model illustrated below. Let μ Alive 0 Dead-Accident Dead-Other Causes 2 10-5 and μ 7.4 x 10-5 and c = 1.05. Let = max (5,7). Calculate: (i) TP 00 (ii) po (iii)+p 01 A+ Bc for all x where A = 5 x 10-4, B =arrow_forward
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