3. Find the general solution of the system of differential equations d X = dt 8 -5 X 10 cos(7t) – 7 sin(7t) 10 cos(7t) + 8t°e7t ( 7 cos(7t) + sin(7t) ). 10 sin(7t) + 4t³e7t Hint: The characteristic polynomial of the coefficient matrix is 1² – 14X + 98. Moreover X,(t) = t*e7t ( cos(7t) – 7 sin(7t) 10 cos(7t) 7 cos(7t) + sin(7t) 10 sin(7t) +t°e7t is a particular solution of the system.

Q: A particular solution of y"-y'-6y=2sin(3x) cos(3x)-5sin(3x) -cos(3x)-3sin(3x) a. b. 8 13 C.…

A:

Q: he following function: =: Find fxy. f(x, y) = 5x4y6x4y5 - 21

A:

Q: Given that Y1 = x-1/2 cos x and y2 = x-1/2 sin x from a fundamental set of solutions of (--)- x²y" +…

A:

Q: Use the method of variation of parameters to find a particular solution of the following…

A: Given,             y''+36y=sin5x.

Q: Solve the following differential equations 1) 2) 3) dy +4x +2y = 0, dx² dx dy 2d²y dr² dx -5x +9y=0,…

A: Since you have uploaded multiple part questions according to our guidelines we have solved first…

Q: Consider the system of differential equations xi(t) = 3x₁ (t) + 2x2(t) x₂ (t) = x1(t) + x₂(t) + e²t…

A:

Q: Suppose that for a 2 x 2 matrix A, Au = 30 for = • How is the pair (3, ū) called for a matrix A?…

A: Given: Av→=3v→ for v→=-1-1. Consider the matrix A as abcd Av→=abcd-1-1=-a-b-c-d If a+b=c+d, then…

Q: Suppose that for a 2 x 2 matrix A, AF= 35 for 7 = • How is the pair (3, 7) called for a matrix A?…

A:

Q: Which of the following functions are solutions to the 1-D heat equation? Ut = guxx Ou= 2-36t cos(3x)…

A: Given: We will be checking the answers one by one. For : Here,                ut=∂ ∂…

Q: 3. Find the general solution of the system of differential equations d X = dt 8. -5 10 cos(7t) – 7…

A:

Q: Solve the following differential equations 2d²y dx² d²y dy dx² dx dy 1) 2) 3) 4) 5) x² +4x +2y = 0,…

A:

Q: dX Find for the given matrix function. dt dX dt sin 5t cos 5t cos 5t e-5t X(t) = sin 5t 8 cos 5t…

A:

Q: 4. Solve the given system of differential equations using the derivative operator d²x + y = 2t dt2…

A:

Q: Suppose that for a 2 x 2 matrix A, AŬ= 3õ for ū = How is the pair (3, v) called for a matrix A?…

A: given a matrix A of order 2×2 ,  Av→=3v→ for v→=-1-1 (a) how is the pair 3,v→ called for a matrix A…

Q: 2. What is the solution of a 3rd order homogeneous linear ODE whose roots of the characteristic…

A: Given,  A solution of third order homogeneous linear ODE whose roots of the characteristics equation…

Q: The solution to the IVP, is x₁ = 13x1 x2, x1(0) = x2 = 34x1+7x2, x2(0) = -1 x1(t) = e10t (cos(5t) +3…

A:

Q: -4 Find the general solution to the second order system x' " х+ -5 cos(2t). 2

A:

Q: 3. Find the general solution of the system of differential equations d. 8 -5 = x* cos(7t) – 7…

A:

Q: Use the method of variation of parameters to find a particular solution of the following…

A: We find Use the method of variation of parameters for the particular solution.And wronskian w

Q: 5. Find ALL degree solution of 3sin 0 + 3 = 2 cos' 0.

A:

Q: 11. Find the general solution of uyy - 4xu, = cos 2y – 2x sin 2y + 4x.

A:

Q: Use the method of variation of parameters to find a particular solution of the following…

A:

Q: Use the method of variation of parameters to find a particular solution of the following…

A: