For Problems 1-7, show that the given functions are solutions of the system
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Differential Equations and Linear Algebra (4th Edition)
- Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.arrow_forwardYou learnt from chemistry and ECH 3023 that hydrogen sulfide may be reacted with sulfur dioxide in a sulfur recovery raector in accordance with the equation: a H2 S + b SO2 → c S + d H2O Find the smallest positive integer values of the stoichiometric coefficients a, b, c and d by setting up a set of linear system of equations from the atomic balances and solving the linear system using Gauss elimination and back substitution. Show the details of your work.arrow_forwardSolve the following system dx -4x + 2y dt dy = -x - y dtarrow_forward
- Find a real general solution of the system - (: :) () d 1 6 dt (y 4 3arrow_forwardConsider a normal, homogeneous, constant coefficient system of differential equations: yi = ay1 +A12Y2 +arrow_forwardFind the real-valued general solution to the following systems of equations 2 -5 x'(t) = ({arrow_forward
- Find the general solution of the following linear system: [1] 4 3 y' = yarrow_forwardWrite the given system as a set of scalar equations. Let x' = col (x1'(), x2 (1), x3'(1)- 0 10 1 2 x' = 0 0 1 x+t - 1 1 -11 4 .... X1 (t) = x2'(t) = X3 (t) =arrow_forwardFind general solutions to the linear system. Use the method of polynomial differential operators, finding the determinant and roots, and then substituting in the original first equation to eliminate extra coefficients. x′=−x+3y,y′=2yarrow_forward
- This is the first part of a two-part problem. Let P = cos(6t) y(t) = |- (sin(6t)) | -6 sin(6t) , Y2(t) = -6 cos(6t) a. Show that y1 (t) is a solution to the system y = Py by evaluating derivatives and the matrix product (t) -6 0 Enter your answers in terms of the variable t b. Show that y2 (t) is a solution to the system y = Pj by evaluating derivatives and the matrix product y2(t) Enter your answers in terms of the variable t.arrow_forwardSolve the given linear system. -- X + 1 3 1 2t X' = -1 1 X(t) =arrow_forwardUse the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. (D+3)[u] (D+3)[v] = et (D-1)[u] + (4D+1)[v] = 7arrow_forward
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