The general solution of y000 −4 y00 + y0 + 6 y = 0 is: (Hint: r = 2 is a root of the characteristic equation)
Solution:
The characteristic equation is
Using synthetic division we have,
The general solution of the given differential equation is
A particular solution of the nonhomogeneous differential equation y00 − 2 y0 − 15 y = 2 cos 3x + 5 e5x + 2 will have the form:
Question 3 Find the general solution of "" - 6y" + 117' - 6-0 given that r1 = 2 is a root of the characteristic equation a)y=C22*+&+603 b) y=,22+*+ Cre" c)y=C22*+&+C22 d) -Ce2+Ce*+6633 e)y=e 28+ Ce*+C, f) None of the above. Question 4 Find the general solution of "" – 3y" - Dy' + 27y=0 given that rı = -3 is a root of the characteristic equation. a) y=C2*+Cxé* +22 b) y=Ge4+Ce**,62* c) y= 3 + x +c, d) y=C+*+Cre*+,231...
Find the general solution of the following equation. y"' +3y"-4y' - 12y =0. (Hint: Rational root test)
I. (a) Find the general complex solution for the following homogeneous equation: y"-y" + 81/ + 10y = 0. (One root of the characteristic polynomial is λ| =-1.) Your solution must have three (complex) integration constants. (b) Because the coefficients of the equation are real, it makes sense to ask what is the most general real solution. Obtain it by separating the real part of the solution you found in (a). Your result must have three real integration constants 2....
(15 pts) Find the general solution of the following equation. y" +5y"+ 3y - 9y 0. (Hint: Rational root test)
Find the general solution of the given differential equation y(6) + y" =0 Find the general solution of the given differential equation y''' +3y" + 3y' + y = 0
Use the reduction of order to find the general solution. 3 y0, yn (0, 00). 3 y0, yn (0, 00).
Problem 6 Solve the following IVP: a) y" – 4y" +20y'=0 ; y0)=2 , y'(0)=0, y"(0) = 6 b) y" +4y=0; y(0)=2 , y'(0) = 3
(1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has a regular singular point atx 0. The indicial equation for x 0 is 2+ 0 r+ with roots (in increasing order) r and r2 Find the indicated terms of the following series solutions of the differential equation: x4. (a) y =x (9+ x+ (b) y x(7+ The closed form of solution (a) is y (1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has...
Find the general solution of the equation: y'' + 5y = 0 Find the general solution of the equation and use Euler’s formula to place the solution in terms of trigonometric functions: y'''+y''-2y=0 Find the particular solution of the equation: y''+6y'+9y=0 where y1=3 y'1=-2 Part 2: Nonhomogeneous Equations Find the general solution of the equation using the method of undetermined coefficients: Now find the general solution of the equation using the method of variation of parameters without using the formula...