Mathematical Physics 2 H.W.4 y"+y-6y y+4y+4y y"+y0 y(0) 2 and y '(0) Subject to the initial conditionns 1 y"-y0 y(0) 2 and y'(0) = 1 Subject to the initial conditions yy'-12y 0 y(0) 2 and y '(0) 1 Subject to the initial conditions y"-4y xe Cos2x y"-2y'x+ 2e y"+y=sinx "-4y'+13y= e cos3x Solve the boundary-value problem y(0) = 1 and y(1) = 3 y"+ 2y'+y=0 Solve the initial-value differential equation y"+ 4y'+4y=0 subject to the initial conditions y (0) =...
Problem 1: Solve the initial value problems: a 2y" – 3y' +y=0 y(0) = 2, 7(0) = 1 by' + y - 6y = 0 y(0) = -1, y'(0) = 2 cy' + 4y + 3y = 0 y(0) = 1, y'(0) = 0 Problem 2: Solve the initial value problems: a y' +9y = 0 y(0) = 1. 1'(0) = -1 by" - 4y + 13y = 0 y(0) = 1, y'(0) = 3 cy" + ly + ly...
homo 2nd order linear equations is necessarily the number -b/2a)]. 1. Find the general solution to the following homogeneous differential equations. (a) y" - 2y + y = 0 (b) 9y" + 6y + y = 0 (c) 4y" + 12y +9y = 0 (d) y' - 6y +9y = 0 2. Solve the the following initial value problems. (a) 9y" - 12y + 4y = 0 with y(0) = 2 and y(0) = -1 (b) y' + 4y +...
3) Solve the initial value problem. a) nie - 2x(y2 – 2y) = 0, with y(0) = 4 b) (-4y cos x + 4 sin I Cos I + sec? x)dx + (4y - 4 sin x)dy = 0, with y ) = 1
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition: For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
Let Lyl = y + 2y + y (a) Solve the initial value problem L[y]=0 y(0)=1 (y'0)=1 (b) Use the method of undetermined coefficients to find a particular solution to the equation L[y] =2e-4
Solve the initial value problem y" - 6y' + 13y = 0, y(0) = 0, y'(0) = 1.
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 the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
(10 point) Solve the following initial value problems. a) y"+ 4y' + 8y = 40cos(2x), y(0) = 8, y'(0) = 0 b) y" + 6y' + 13y = 12e-3xsin(2x), y(0) = 0, y'(0) = 0 (10 point) Find a general solution of each of the following nonhomogeneous equations. a) y" + 4y = 12x−8cos(2x) b) y(4)− 4y" = 16+32sin(2x)