(Variation of Parameters) (a) Find the two independent solutions x, (1) and x2 (t) of the homogen...
Question 14 Use the method of variation of parameters to find a particular solution using the given fundamental set of solutions {x1,x2}. x′=(−10−1−1)x+(−25t), x1=e−t(01), x2=e−t(−1t) (Enter the solution as a 2x1 matrix.) xp(t)= Question 14 Use the method of variation of parameters to find a particular solution using the given fundamental set of solutions (xi,x2 (Xi, X2l x'=(-1 0 1-1 (Enter the solution as a 2x1 matrix.) Xp (t) =
Use the variation of parameters formula to find a general solution of the system x' (t) = Ax(t) + f(t), where A and f(t) are given. 4 - 1 4 + 4t Let x(t) = xn (t) + xp (t), where xn (t) is the general solution corresponding to the homogeneous system, and xo(t) is a particular solution to the nonhomogeneous system. Find Xh(t) and xp(t). Xh(t) = U. Xp(t) = 0
Use the method of variation of parameters to find a particular solution of the following differential equation. y" - by' +9y = 2e 3x What is the Wronskian of the independent solutions to the homogeneous equation? W(11.72) = 0 The particular solution is yp(x) =
Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) + f(t), where A and f(t) are given. 2 A= -4 2 ,f(t) = -1 14 +2t - 1 Let x(t) = x (t) + X(t), where xn(t) is the general solution corresponding to the homogeneous system, 1 xp (t) is a particular solution to the nonhomogeneous system. Find xh (t) and xp(t). and 1 -2 Xh(t) = 41 2 1 1 X(t)...
3 multiple choice questions Two solutions to a second order differential equation are linearly independent if (a) their Wronskian determinant is zero. (b) their Wronskian determinant is nonzero. (c) they are not scalar multiples of one another. (d) they each have a corresponding initial condition. (e) Both (b) and (c) are correct. Given the differential equation y"+9y' = e-91, the correct guess for a particular solution would be (a) yp = Ae-94 (b) yp = (Ax + B)e-9r. (c) yp...
1. Use the method of variation of parameters to find a particular solution x, using the given fun- damental set of solutions {x1, x2}. *= ( = -1)x+(%) x1=e*(), x=e*(+)
Use the variation of parameters formula to find a general solution of the system x'(0) AX(t) + f(t), where A and f(t) are given -4 2 А. FU) 21 12 +21 Let x(t) = xy()+ X(t), where x, (t) is the general solution corresponding to the homogeneous system, and X(t) is a particular solution to the nonhomogeneous system. Find X. (t) and X.(1).
(1 point In general for a non-homogeneous problem y' + p(x) +(z) = f() assume that y. is a fundamental set of solutions for the homogeneous problemy" p(x) + (2) 0. Then the formula for the particular solution using the method of variation of parameters is where (z)/ and ()/() where W() is the Wronskian given by the determinant W (2) (2) W2) 31(2)/(2) dr. NOTE When evaluating these indefinite integrals we take the W(2) So we have the de...
(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of 2 parts correctly. Consider the differential equation: 9ty' - 2t(t +9)y +2(t+9) y = -26, t>0. You can verify that yı = 3t and y2 = 2texp(2t/9) satisfy the corresponding homogeneous equation. a. Compute the Wronskian W between yı and 32- W(t) = b. Apply variation of parameters to find a particular solution. Bre,+2te (*),+22
Use variation of parameters to find the general solution of the following equation, given the solutions Y1, Y2 of the corresponding homogeneous equation: xy" - (2x + 2)y + (x + 2)y = 6x3e", Y1 = e", y2 = x3e".