2. (10 points) Use reduction of order to find a second (non-trivial) solution up to the...
1- Use the Reduction of Order method to find a second solution of the equation 4x2y" + y = 0 Given that yı = xì Inx 2- Solve the differential equation y" + 4y + 4y = 0 3- Solve the differential equation y" + 2y + 10y = 0 y” + 5y + 4y = cosx + 2e*
The indicated function yı() is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, Y2 = vy() / e-SP(x) dx dx (5) y?(x) as instructed, to find a second solution y2(x). x?y" + 2xy' – 6y = 0; Y1 = x2 Y2 The indicated function yı(x) is a solution of the given differential equation. 6y" + y' - y = 0; Y1 Fet/3 Use reduction of order or formula (5) in Section...
(9 points) Use the Reduction of Order Formula to find a second linearly independent solution to the DE given by xay" + 2x y' - 2y = 0, if y, (x) = x is one solution of the DE.
Previous Problem Problem List Next Problem (1 point) Let's find the general solution to z2y"-5zy, + 8y-(2-P) using reduction o of order (1) First find a non-trivial solution to the complementary equation z' smaller power m. 5zy' +8y0 of the form z. There are two possibilities, pe (2) Now set u = tizm and determine a first order equation (in standard form) that ,' t' must satisfy (3) Solve this for z using cl as the arbitrary constant 4) Solve...
Find a second solution of the given differential equation y2(x). Use reduction of order or formula. y"- 6y'+25y =0; y1=23cos(4x)
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
7. Use the method of reduction of order to find a second solution of the differential equation xy" - y + 4x³y = 0, x > 0; y1(x) = sin x².
1. For each question: i) verify that yı(2) is a solution. ii) Use reduction of order to find the general solution. iii) Find a fundamental solution set. iv) Find the Wronkskian, and list it's zeroes and discontinuities. Verify that the Wronskian is nonzero and continuous on the given interval. (e) y" + 4y + 4y = 0, yı = -2% (-00,00). () r’y" – 2xy' + 2y = 0, yı = x. (0,00). -
viven ODE (a) use reduction of order to find the general solution of 2. Given that y, = e-2x is a solution of the given ODE (a) use reduction of order DE V V -6m 0: (b) what is the second linearly independent solution, y of the ODEO
4. Method of variable reduction makes use of one of the known solutions of a differential equation to find the other solution. Find the second solution of the given differential equation if one of the solutions is given. Show all steps. If yı:1) = et is one of the solutions, find the other solution of the differential equation using variable reduction. To do this, assume yz(2) = u(2)yı(2) = ue" and then solve the equation by substitution. (1 - 1)y"...