Use the reduction of order method to solve the following problem given one of the solution y1.
(a) (x^2 - 1)y'' -2xy' +2y = 0 ,y1=x
(b) (2x+1)y''-4(x+1)y'+4y=0 ,y1=e^2x
(c) (x^2-2x+2)y'' - x^2 y'+x^2 y =0, y1=x
(d) Prove that if 1+p+q=0 than y=e^x is a solution of y''+p(x)y'+q(x)y=0, use this fact to solve (x-1)y'' - xy' +y =0
Use the reduction of order method to solve the following problem given one of the solution y1. (a) (x^2 - 1)y'' -2xy' +2y = 0 ,y1=x (b) (2x+1)y''-4(x+1)y'+4y=0 ,y1=e^2x (c) (x^...
given y1=x is a solution of the following DEXX+2xy-2y=0, the second solution is x 2 e2 Question 2 2 pts The differential equation whose general solution is Y=CCos(6x)+C2 Sin (V6 x) y" by 0 Oy -6y=0 y +6y=0 y"+6y'=0 2 pts Question 3 given that y1= x1 is a solution, if we use the reduction of order to solve the ODE 2x2 y + xy - 3y=0 we find that u= AXR+B (Ax512 - Ax+B Axe5124B
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). y'' + 2y' + y = 0; y1 = xe−x y2 =
use the fact that y=x is a solution of the homogeneous equation x^2y''-2xy'+2y= 0 to completely solve thee differential equation x^2y''-2xy'+2y= x^2
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*
1) Use the reduction of order method to solve the following problems given one of the solutions yı: 2x²y” +3xy'-y=0 given y=Vx is a solution to this ODE
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). -
Use the method of reduction of order to find the general solution to x2r"-xy'+y =x given that 3'1 = x is a solution to the complementary equation 1. Use the method of reduction of order to find the general solution to x2r"-xy'+y =x given that 3'1 = x is a solution to the complementary equation 1.
given that y1= e3x is a solution, if we use the reduction of order to solve the ODE y" + =6y'+9y=0 we find that u Ax+B Ax+B)e-3x) -3x e Ax
9. Solve the IVP with Cauchy-Euler ODE: xy"txy+4y-0; y(1)-o, y )--3 = 0 , use Variat 0 10. Given that y = GXtar2 is a solution of the Cauchy-Euler ODE x, "+ 2xy-2 Parameters to find the general solution of the non-homogeneous ODE y+2xy-y homogeneoury"rQ&)e-ar)-
Given: y''+2y'=2x+5-e^-2x General solution is: y=c1e^-2x+c2 +1/2(x^2)+2x+1/2(xe^-2x) Solve using the method of undetermined coefficients and show all steps please! I have the form of yp is Ax^2+Bx+Cxe^-2x, and the issue that plagues me is in solving for A B C. I get A=1/2 and I get B=2, but the terms involving C fall off the face of the earth when I substitute y' and y'' of the solution form into the equation, so how can I solve for C? Help...