Verify that the vector X is a particular solution of the given nonhomogeneous linear system x'...
Verify that the vector Xa is a particular solution of the given nonhomogeneous linear system. ,_21 et+ 1 tef, one has 1 te is a particular solution of the given system Since the above expressions--Select Need Help?Read It Talk to a Tutor dx dt x(t), y(t)) Need Help?Read It Watch It Talk to a Tutor
-15 POINTS Verify that the vector Xis a particular solution of the given nonhomogeneous linear system. x=(!)x-(1)•: x-(-)*+(-) for x,-(1)+(-3)... one has 2. *-(t)oi+() of cha particular so Since the above expressions - Select
Verify that the given vector is the general solution of the corresponding homogeneous system, and then solve the nonhomogeneous system. Assume that t> 0. bx' = (36 - 16)* +(8524->), x) = 41(2)-3 + c3(3):46 10 = C(1,2)=8+ C,(2,1)e46 +24-3,) + +(2,0) + +15(0,1%) + 234 3:0) +2=23/0,33) 15 X(t) = + + 7
Part A is first 2 lines, Part B is last 2 lines, thanks! For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the functions y(x) and y2(x) are linearly independent solutions ofthe corresponding homogeneous equation. Note: The cocfficient of y" must always be 1, and hence a preliminary division may be required y2(x) = x-2 ·y1(x) = x y2(x) = ex For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the functions...
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. 5 y'' = 2y + 5 cotºx, yp(x) = 3 cotx The general solution is y(x) = (Do not use d, D, E, E, I, or as arbitrary constants since these letters already have defined meanings.)
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. 5 y"' = 2y +5 tan ºx, yp(x) = tan x The general solution is y(x) = (Do not use d, D, e, E, I, or las arbitrary constants since these letters already have defined meanings.)
2. Consider the linear system. where ik -1 3 5 r3 Verify that gives a particular solution to the system. Then use this to find the general solution x by solving the hmogenous equation A x0 13 51o 6 -| 3 SiO 0
Consider the following nonhomogeneous system for 2-dimensional vector X(t), t 2 0. 0 x(0)1 2 -1 where A- 5 -2 (a) Use the Laplace transform to compute eAt. (b) Using eAt of (a), find the solution of the above nonhomogeneous system Consider the following nonhomogeneous system for 2-dimensional vector X(t), t 2 0. 0 x(0)1 2 -1 where A- 5 -2 (a) Use the Laplace transform to compute eAt. (b) Using eAt of (a), find the solution of the above...
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. y" + 5y + 6y = 24x2 + 40x +8+ 12 e*. Yp(x)= e* + 4x? The general solution is y(x) = 0 (Do not use d, D, e, E, I, or las arbitrary constants since these letters already have defined meanings.)
8. Consider the nonhomogeneous linear system of differential equations 1 1 1 -1 u = -1 11 1 1 u-et 1 1 2 3 First of all, find a fundamental matrix and the inverse matrix of the fundamental matrix of the corresponding homogeneous linear system. Then given a particular solution 71 uy(t) = et 1 2 find the general solution of the nonhomogeneous linear system of differential equations. Hint: det(A - \I) = -(1 – 2)?(1+1)