3. Verify that equation (5) is a solution to equation (4). This can be done by...
please help! 7. Consider the generalized Pell equation x2- 6y2 =3. *) Verify that 3+ v6 E Z[V6] gives a solution of (*). Produce three other non-trivial positive solutions of (. (Hint: Use solutions of x2 - 6/2 = 1 to help out.) 7. Consider the generalized Pell equation x2- 6y2 =3. *) Verify that 3+ v6 E Z[V6] gives a solution of (*). Produce three other non-trivial positive solutions of (. (Hint: Use solutions of x2 - 6/2 =...
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
3. Find the general solution of the given differential equation: (15 points) Hint: verify if m-l is a root of the auxiliary polynomial 3. Find the general solution of the given differential equation: (15 points) Hint: verify if m-l is a root of the auxiliary polynomial
Please work out so I can verify I've done it correctly. Thanks 3. Consider a system with the following state equation h(t)] 1-2-1-3] 1x3(t)] 11 Use MATLAB to (a) Let 0-13x3 and solve the Lyapunov equation to find P matrix (use lyap command. Note that this command takes A and Q as its inputs, not A and Q) whether the state equation is asymptotically stable or not. eigenvalues. Does the result match your answer to part (b)? (b) Find the...
2) (25 points) a) (5 points) Verify that y= eat is a solution of the homogeneous differential equation y" - 12y' + 36 y = 0. b) (15 points) Use the method of reduction of order to find a second solution 72 of the given homogeneous equation and a particular solution y of the nonhomogeneous differential equation y" - 12y' + 36 y = 36. e) (5 points) Can you write the general solution of the nonhomogeneous differential equation y"...
Let [ 2 1 4 ܠܛܙ A= -3 -4 and 7= [ 3 2 Verify that the linear system Až=ū is inconsistent. Let r = and Explain why neither 7 nor y is a least-squares solution for A and 5, without finding the actual solution(s). [Hint: Compute Aē and Ay and compare them with 6.]
Verify by substitution that the given function is a solution of the given differential equation. Note that any primes denote derivatives with respect to x. y' = 4x3y = x + 6 What step should you take to verify that the function is a solution to the given differential equation? O O O O A. Substitute the given function into the differential equation, B . Integrate the function and substitute into the differential equation C . Determine the first and...
(b) (Problem 7.8.19 in textbook, slightly modified) Compute the general solution of the ODE 5 3-2 85 -4 4 33 (Hint: You may verify and exploit the fact that (A I)2 0.) (b) (Problem 7.8.19 in textbook, slightly modified) Compute the general solution of the ODE 5 3-2 85 -4 4 33 (Hint: You may verify and exploit the fact that (A I)2 0.)
First, verify that y(x) satisfies the given differential equation. Then, determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition. y' =y+3; y(x) = CeX-3; y(0) = 8 What step should you take to verify that the function is a solution to the given differential equation? O A. Differentiate...
(a) Find the solution to Laplace's equation on a disk with boundary condition u(1,0) = 5 + sin(40). (You do not need to derive the general solution to the polar Laplace's equation.) (b) Verify that the solution to (a) satisfies the mean value property. (Hint: compare the average value of u(r, ) on the boundary r=1 to the value of u(r,() at r = 0.) (c) Find the minimum and maximum of the solution to (a) and verify they occur...