Solve the initial-value problem 2y" + 5y' - 3y = 0, y(0) = 3, y'(0) = 5.
non-homo 2nd order linear equations 1. Find the general solution for each of the following differential equations (10 points each): (a) (b) (e) y" – 2y! - 3y = 3e2x y" — y' – 2y = -2.3 + 4.2? y" + y’ – 67 = 1234 + 12e-2x y" – 2y' – 3y = 3.ce-1 y" + 2y' + y = 2e- (Hint: you'll use Rule 7. at least once) (e 2. Find the solution to the following differential equation...
differential equations .. Boundary Value. Solve the following: y" + 2y' - 5y = 0, y(0) = 0, y'(1) = 0 F. Boundary Value. Solve the following: y" + 2y' - 3y = 9x, y(0) = 1, y'(1) = 2
Solve 2y'' – 5y' – 25y = 0, y(0) = -6, y'(0) = – 15 (t) = Consider the initial value problem y' + 3y' – 10y = 0, y(0) = a, y'(0) = 3 Find the value of a so that the solution to the initial value problem approaches zero as t + oo a = 1
2nd order linear homogeneous Find the general solution to the following homogeneous differential equations (you answers must have two arbitrary constants (you may use any letters, for example p and q or m and n instead of ki and k2 - notation doesn't matter here]). y" + 2y' – 3y = 0 (b) 6y" – y-y=0 (c) y" + 5y = 0 (d) y" - 9y' +9y 0 The two constants, e.g. ki and k2, determine (and are determined by)...
Can you please show number #25, #27 (Please make work readable) 21. y" + 3y" + 3y' + y = 0 22. y" – 6y" + 12y' – 8y = 0 23. y(a) + y + y" =0 24. y(4) – 2y" +y=0 In Problems 1-14 find the general solution of the given second-order differential equation. 1. 4y" + y' = 0 2. y" – 36y = 0 3. y" - y' - 6y = 0 4. y" – 3y'...
5. Find the general solution of the following differential equations: (a) 6"-5y y 0 (b) 4y"+12y9y 0 (c)2" 3y 6. Solve the following initial value problems:
Differential Questions problem. Can someone help. Thanks. 1. Consider the initial valuc problenm ay + 5y-cost, y(0) = 1. Solve the IVP using THREE DIFFERENT METHODS. 2. Solve the following differential equations. If there are initial values, solve the IVP. If there are not, find the general solution. (a) (2x + y)dr + (Zy +エ)dy = 0, y(2) =-3; (o) du) dx 2y +4y 3. Solve the following initial value problems y" + 2/ + 5y = 0, y(0) =-1,...
No 4. Solve the differential equation dy dx . Solve the initial value problem: y" + 3y' + 2y 10 cosx, y(0) 1,y'(0) 0
25 &27 In Problems 15-28 find the general solution of the given higher-order differential equation. 15 y" – 4y" – 5y' = 0 16. y' – y = 0 y'' – 5y" + 3y' + 9y = 0) 18. y' + 3y" – 4y' - 12y = 0 30 d²u 19. d13 + d²u - 2u=0 dt? d²x d²x an de dt2 4x = 0 21. y' + 3y" + 3y' + y = 0 22. y" – 6y" +...
please answer all questions and show all working 2. Solve the the following differential equations (you answers will not have any arbitrary constants) (a) y"+y' - 2y =0 with y(0) 1 and y(0) = 1 (b) 6y" - 5y + y =0 with y(0) = 4 and (0) = 0 (c) y" + 5y + 3y = 0 with y(0) = 1 and y(0) = 0 (d) y" + 8y' - 9y=0 with y(1) = 1 and y(1) = 0