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Section 7.4 Basic Theory of First order Linear systems: Problem 2 Previous Problem Problem List Next...
Solve the system of first-order linear differential equations. (Use C1, C2, and C3 as constants.) Y1 3y2 Y2' 4y1 4y2 + 1473 7y3 = Y3' = 473 (y1(t), y2(t), y(t)) Need Help? Read It Watch It Talk to a Tutor [1/3 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.4.029. Write out the system of first-order linear differential equations represented by the matrix equation y' = Ay. (Use y1, and y2, for yi(t), and yz(t).) [01] Yı' = Y2' =
Previous Problem Problem List Next Problem (1 point) Consider the linear system -3 -2 >= -3) y. 5 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. di = on = and 12 = · U2 b. Find the real-valued solution to the initial value problem { vi = -3yı – 2y2, 5yı + 3y2, yı(0) = 11, y2(0) = -15. y۔ = Use t as the independent variable in your answers. yı(t) = y2(t) =
Please show all your work HW3: Problem 7 Previous Problem Problem List Next Problem (1 point) Fundamental Existence Theorem for Linear Differential Equations Given the IVP dz1 d"y d" - 4.(2) +4-1(2) +...+41 () dy +40()y=g(2) dr y(t) = yo, y(t)= y yn-1 (3.) = Yn1 If the coefficients (1),..., Go() and the right hand side of the equation g(1) are continuous on an interval I and if (1) #0 on I then the IVP has a unique solution for...
Previous Problem Problem List Next Problem (1 point) Note WeBWork will interpret acos(z) as cos (z), so in order to write a times cos(z) you need to type a cos(z) or put a space between them. The general solution of the homogeneous differential equation can be written as e-acos(x)+bsin(z) where a, b are arbitrary constants and 1r is a particular solution of the nonhomogeneous equation By superposition, the general solution of the equation y" + ly-2ez is บ-Uc + so...
2. (Sturm-Liouville Theory) Consider the following linear homogeneous second-order differential equation and boundary conditions v(T where a and b are finite, p(x), p(x,)) are real and continuous on [a, b), and p(x),w(x) > 0 on a,b]. Show that two distinct solutions to this ODE, Pm(z) and (x), are orthogonal to each other on the interval [a,b]. That is, prove the following relationship 0 2. (Sturm-Liouville Theory) Consider the following linear homogeneous second-order differential equation and boundary conditions v(T where a...
Section 3.2 The Wronskian: Problem 5 Previous Problem Problem List Next Problem (1 point) Determine the largest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution. d2x sin(t)atx + cos(r)ar + sin(,)x = tan(t), dx x(0.5)-8, x,(0.5)-10 Interval Section 3.2 The Wronskian: Problem 5 Previous Problem Problem List Next Problem (1 point) Determine the largest interval in which the given initial value problem is certain to...
3.3-Complete Solution to Linear Systems: Problem 2 Previous Problem Problem List Next Problem (1 point) Solve the system { x1 | 4x1 +x2 +4x3 = +502 –2x3 = -9 6 23
HW3.2: Problem 1 Previous Problem Problem List Next Problem (1 point) Given a second order linear homogeneous differential equation a2(x)y" + ai (x)y' + ao (x)y0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions yi, y2. But there are times when only one function, call it y, is available and we would like to find a second linearly independent solution. We can find 2 using the method of reduction of order. First,...
HW03 linear systems: Problem 6 Previous Problem Problem List Next Problem 1 point) Solve the system y-11 714y35 If there is no solution, enter NONE in both answer blanks. Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email instructor
Section 7.1 Introduction First Order Systems: Problem 5 Previous Problem Probiem List Next Problem (1 poing) Consider two interconnected tanks as shown in the figure above. Tank 1 Initial contains 10 L Olters) of water and 170 g of salt. while tank 2 Initiaily contains 60 L of water and 445 g of salt. Water containing 25 g'L of salt is poured into tank1 at a rate of 4 U/min while the mixture flowing into tank 2 contains a salt...