5. (10 points) Use the Variation of Parameters method to find the particular solution yp(2) of...
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) =
7. (10 points) Find a particular solution yp(t) to the nonhomogeneous equation ty + y - y = 24t*, t> 0, given the fact that the general solution of the associated homogeneous equation is yn(t) = cit + cat-, C1, C2 E R
2. Use variation of parameters to find the general solution y and the particular solution yp. 6) y" + 2y' +y= .73
use variation of parameters to find a particular solution yp(x) y" + 6y + 8y = e2x dx + y2() San f(x)y2(x) f(x)yı(2) Recall that, yp(x) = -41(x) dr. aW(41, 42) aW(41, 42) If you use the method of undetermined coefficients you will receive zero credit.
please give the correct answer with explanations, thank you Find a particular solution, yp(), of the non-homogeneous differential equation d2 y (2) +6 (de y(x)) +9y (x) = -12 , d22 given that yn (r) = A e-31+B 1 e 30 is the general solution of the corresponding homogeneous ODE. The form of yp() that you would try is Yp = ax + 6 yp = 2040 O yp=0x2-32 Enter your answer in Maple syntax only the function defining yp()...
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) =
10. Use the Method of Variation of Parameters to find a particular solution for the differential equation y" +y= ex (You may use the integral formulas Íe' sin xax= ex (sin x-cos x) + c and「' cos xdr= e"(sin x + cos x) + c. )
1. Use the method of variation of parameters to find a particular solution to the equation below. Then use your particular solution to find a general solution to the equation. -10et y" – 2y' + y = 72 +4
3) Solve for the following ODE using Variation of Parameters y' – 4y' + 4y = x?e? a) Determine the characteristic equation and its roots, and solve for the complementary solution yn (6 marks) b) Solve for particular solution Yp using Variation of Parameters (13 marks) c) What is the general solution y ? (1 mark)
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*(+)