Applied Differential Equations 2. For which parameters a and b the zero solution of the following...
1. Solve the following Differential Equations. 2. Use the variation of parameters method to find the general solution to the given differential equation. 3. a) y" - y’ – 2y = 5e2x b) y" +16 y = 4 cos x c) y" – 4y'+3y=9x² +4, y(0) =6, y'(0)=8 y" + y = tan?(x) Determine the general solution to the system x' = Ax for the given matrix A. -1 2 А 2 2
QUESTION 6 5 points Find the general solution of the following reducible second-order differential equation. Assume x,y and/or y positive where helpful 9y%y"=5 on Ay?+9 (Ax+B) 2-5 ou. Ay?- } (Ax+B) 2-5 ocy2-9(Ax+B)2=5A op. Ay?-(Bx+A) 2-5 OE. Ay?- (Bx+Ay) 2-5
QUESTION 14 Find the general solution of the following reducible second-order differential equation. Assume x, y and/or y' positive where helpful. 9yy"=5 Od Ay?- (Ax+B) 2=5 OB.y2-9(Ax+B) 2=5A oc Ay?+9 (Ax+B) 2-5 00. Ay? 5 (Bx+A) =5 DE Ay? (Bx+Ay) 3=5
QUESTION 9 Find the general solution of the following reducible second-order differential equation. Assume x, y and/or y' positive where helpful. 9y3y" = 5 4. Ay?- (Ax+B)2=5 0 2. Ay?- } (Bx+Ay) 2=5 oc12-9(Ax+B)2=5A OD. Ay2+9 (Ax+B)2=5 Ay?- (Bx+A) ?=5 OL
QUESTION 8 Find the general solution of the following reducible second-order differential equation. Assume x, y and/or y' positive where helpful. 9y3y" = 5 DA. Ay? 1y2-(Bx+Ay)?=5 OB.X2-9(Ax+B) 2=5A OC. Ay?- 5 (Ax+B) 2=5 D. Ay2+9 (Ax+B) 2=5 DE AY?- (Bx+4)=5
Answer all Please! Thanks 1. Confirming Solutions to Differential Equations: Verify that each function does in fact solve the given differential equation. If there are parameters in the function (A. b. k), give the range of values of those parameters for which that function is a solution. The prime indicates differentiation with respect od dr' (b) y" + 4y = 0; y = A sin(kx + φ). (c) y"-4s, + 4y = 0, y = Axe . (d) x2y', +...
Differential Equations Assignment 15. Variation of Parameters Solve each of the following by variation of parameters 1-4 please Assignment 15. Variation of Parameters Read 4.6, 6.4 You should be able to do the following problems: Exercise 4.6 Problems 1 18, Exercise 6.4 Probl1-6 Hand in the following problems: Solve each of the following by variation of parameters. y" +y - sin a cos r 2a 3 4. The Method of Variation of Parameters can be used to find the general...
a,b, and c 1. Determine if the following function is a solution of a differential equation. a) y = 4e2' + Be for 6y"- 7y3y = 0 (3pts) b) y = Ae* + Be*** + 2 sin (3x) for y"+y'-6y=6cos(3x) – 30sin (3x) (3pts) c) y = Ae?" + Bx? for y"- 3y + 2y = 0 (3pts)
(24 points) Find the general solution to each of the following differential equations dy a) = e)(x - 2). Over what interval is this solution valid? dx b) y" - 2y + y = (Hint use the method of variation of parameters) 1 + x2 c) y" - 8y' + 17y = 0. Is this solution (i) undamped, (ii) critically damped, (iii) under-damped, or (iv) over-damped?
O A Ay21 OB Ay?- (Bx+Ay) ?=5 Find the general solution of the following reducible second-order differential equation. Assume x, y andor y positive where helpful. 9yy"=5 (Bx+A) 3-5 9 9 ocy2-9(Ax+B)2=5A 2- 5 (Ax+B) 2=5 O E Ay2+9 (Ax+B)2=5 OD. Ay?-