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-15 POINTS Verify that the vector Xis a particular solution of the given nonhomogeneous linear system....
Verify that the vector X is a particular solution of the given nonhomogeneous linear system x'...
Verify that the vector X is a particular solution of the given nonhomogeneous linear system x' 2 1 Xo - 13 For X, , one has Since the above expressions -Select-- te is a particular solution of the given system
Verify that the vector Xa is a particular solution of the given nonhomogeneous linear system. ,_21...
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
Verify that the given vector is the general solution of the corresponding homogeneous system, and then...
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
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation....
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. 592 0"' +20' - 630 = 1 -21, 0p(t) = -3 The general solution is e(t) = (Do not use d, D, e, E, I, or as arbitrary constants since these letters already have defined meanings.)
8. Consider the nonhomogeneous linear system of differential equations 1 1 1 -1 u = -1...
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)
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation....
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.)
Consider the following 2nd order nonhomogeneous linear equation x 00 + 4x 0 + 5x =...
Consider the following 2nd order nonhomogeneous linear equation
x 00 + 4x 0 + 5x = cos 2t
1. Solve for the fundamental solutions of its associated
homogeneous equation.
2. Find a particular solution of the nonhomogeneous
equation.
3. Based on your answer to the previous two questions, write
down the general solution of the nonhomogeneous equation.
Problem II (15 points) Consider the following 2nd order nonhomogeneous linear equation x" + 40' + 5x = cos 2t 1. (6 points)...
4. Consider the nonhomogeneous linear system of differential equations / 4 3 4t / cos(3t) +...
4. Consider the nonhomogeneous linear system of differential equations / 4 3 4t / cos(3t) + 2te4t / l - sin(3t) / + 4tºe4t / sin(3t)) 43.4t sin(3) ( cos(3t) ) Given a particular solution t²4t / t th 4t / Find the general solution of the nonhomogeneous system. Hint: det(A – XI) = 12 – 81 + 25.
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation....
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. y" - y = 5t, yp(t) = -51 The general solution is y(t)= (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....
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. y" -y= 11t, y(t) = - 110 The general solution is y(t) = (Do not used, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)
Verify that the vector X is a particular solution of the given nonhomogeneous linear system x' 2 1 Xo - 13 For X, , one has Since the above expressions -Select-- te is a particular solution of the given system
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
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
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. 592 0"' +20' - 630 = 1 -21, 0p(t) = -3 The general solution is e(t) = (Do not use d, D, e, E, I, or as 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)
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.)
Consider the following 2nd order nonhomogeneous linear equation
x 00 + 4x 0 + 5x = cos 2t
1. Solve for the fundamental solutions of its associated
homogeneous equation.
2. Find a particular solution of the nonhomogeneous
equation.
3. Based on your answer to the previous two questions, write
down the general solution of the nonhomogeneous equation.
Problem II (15 points) Consider the following 2nd order nonhomogeneous linear equation x" + 40' + 5x = cos 2t 1. (6 points)...
4. Consider the nonhomogeneous linear system of differential equations / 4 3 4t / cos(3t) + 2te4t / l - sin(3t) / + 4tºe4t / sin(3t)) 43.4t sin(3) ( cos(3t) ) Given a particular solution t²4t / t th 4t / Find the general solution of the nonhomogeneous system. Hint: det(A – XI) = 12 – 81 + 25.
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. y" - y = 5t, yp(t) = -51 The general solution is y(t)= (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. y" -y= 11t, y(t) = - 110 The general solution is y(t) = (Do not used, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)
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