Solve the differential equation: 36x²y" + 36xy' + 16y = 0 y= clæ4 + c2.24 in...
a. Find a particular solution to the nonhomogeneous differential equation y" + 16y = cos(4x) + sin(4x). Yo = (xsin(4x))/8-(xcos(4x))/8 help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use ci and C2 in your answer to denote arbitrary constants. Enter c1 as c1 and C2 as c2. Un = c1cos(4x)+c2sin(4x) help (formulas) c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 3 and y'(0) = 2. y...
2. a) Solve the differential equation: 2²/" - 6xy' = 27 6 Oy=4 +6226 + Ins 6 36 Oy=c+ c2 26 76 36 + In 3 6 6 27 Oy=4+ c227 + In 7 ...7 49 Oy=q+cqz? 27 In 2 49 +7 None of the above b) Solve the differential equation: 9z+y" + 9xy' +25y = 0 Oy= cos(5 ln /3) + sin(5 In 3/3) Oy=425 +2.23 Oy=C1 cos(52/3) + 2 sin(5x/3) y=4125 + c2205 in None of the above...
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given D2y + 25y = -5 sin 5x (Let y p = Ax sin 5x + Bx cos 5x.) sin 5x + c2 cos 5x + x sin 5x - 1 x cos 5x Oo oo cos 5x + = x cos 5x y = C1 sin 5x + C2 cos 5x + 5x sin 5x y = C1 sin 5x + C2 cos 5x...
Solve the given differential equation. 9) dy + y = 14 +6 cos 3x 9) dx² B) y = ci sin x + c2 cos A) y=cı sin x +c2 cos x + cos 3x +14 C)y=cı sin x +c2 cos x - cos 3x +14 D) y=q sin x +02 cos x - sin 3x+14
Solve the differential equation: Y" + y = sec(x) given that the complimentary solution is ye(s) = ci cos(x) + c2 sin(x)
Question 2 (15 points) Solve the differential equation for the general solution y 6y' 73y 0 y(t) C cos(3t) C2 sin(3t) y(t) = C1 cos(8t) + C2 sin(8t) y(t) cos(8t) +C2e" sin(St) y(t) Ce cos(8t) Cest sin (8t) y (t) = Cleft cos (8t) + C2eft sin (8t) (t)Cest cos(9)Cesin (9t) Previous Page Next Page Page 2 of9
Find the general solution of the equation y" + 361y = 0. y(t) = C1 cos 19t + c2 sin 19t o o o o y(t) = ci cos t-cı sin t y(t) = ci cos t+ c2 sin 19t y(t) = cı cos 19t+ c2 sin t
Solve the Separable Differential Equation. dy 1) e6x - 6y dx A) y = 6ln (e6x + C) B) y = 6e6x + C y-In (ex.c) D) y = ln (e6x + C) = 4 cos x sec y A) y = sin (4 sin x + C) C) y=sin-1 (4 cos x + C) B) y = sin-1 (4 sin x + C) D) y = 4 sin x + C
Use Variation of Parameters to solve the following differential equations 4) y" + 8y' +16y = e-45 ln(2)
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...