Homework Answers
Note:
If you could not understand the theory in step 01 donnt worry just
remmeber the formula in equation (1) which is used to linearize ode
. If still any doubt regrading any step feel free to ask in comment
section good luck??
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4 Linearize the following ODE around Xo 2T,u,-1 0 0 x 2 sin(x) + xu +...
1. Linearize the following equations: (a) f(x) = x1/3 + cos(x) around x, = 7/2. (b)...
1. Linearize the following equations: (a) f(x) = x1/3 + cos(x) around x, = 7/2. (b) g(x) = -3x3 + sin(4x2) around xo = 2.
Solve the following 1st order ODE: * + 5x = cos(2t) x(0) = 2
Solve the following 1st order ODE: * + 5x = cos(2t) x(0) = 2
2. x" + 6x' + 18x sin 2t, x(0) = -1, x'0) = 1.
2. x" + 6x' + 18x sin 2t, x(0) = -1, x'0) = 1.
2. Use eigenfunction expansion to solve the following IBVP: u,(x, t) ="-(x,t) + (t-1)sin(m), 0 0 ...
2. Use eigenfunction expansion to solve the following IBVP: u,(x, t) ="-(x,t) + (t-1)sin(m), 0
Suppose a system is governed by the following differential equation. Linearize this system about 0 0...
Suppose a system is governed by the following differential equation. Linearize this system about 0 0 radians, radians a. b. 4 Tt radians C. = (t) sin(0(t))u(t) CD
Suppose a system is governed by the following differential equation. Linearize this system about 0 0 radians, radians a. b. 4 Tt radians C. = (t) sin(0(t))u(t) CD
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)...
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:
Solve the following ODE for y(x) y''+y'-2y=sin(2x) y(0)=2 y'(0)=0
Solve the following ODE for y(x) y''+y'-2y=sin(2x) y(0)=2 y'(0)=0
4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u...
4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u (x, 0) ura' (a, t) + 2t sin (2na:) , 0 < x < 1, 0, u(1,t)=0, t > 0, sin(2π.r)-5 sin (4π.r) , 0 < x < 1. t > 0, = = =
4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u (x, 0) ura' (a, t)...
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0<x <c,0 11 (c, 1) = 0, u(x, 0) = f(x), where u is continuous for0sxc,0 and where n is a positive integer. Answer: u(x, 1) Σ A,Jn(gjx) exp (-α,1), where a", and A, are the constants j-1
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0
Solve the given initial-value problem. dax + 4x = -7 sin(2t) + 6 cos(2t), x(0) =...
Solve the given initial-value problem. dax + 4x = -7 sin(2t) + 6 cos(2t), x(0) = -1, x'(0) = 1 xce) = -cos(2+) – sin(2t) + {cos(21) + (sin(21) Need Help? Read It Watch It Talk to a Tutor
1. Linearize the following equations: (a) f(x) = x1/3 + cos(x) around x, = 7/2. (b) g(x) = -3x3 + sin(4x2) around xo = 2.
Solve the following 1st order ODE: * + 5x = cos(2t) x(0) = 2
2. x" + 6x' + 18x sin 2t, x(0) = -1, x'0) = 1.
2. Use eigenfunction expansion to solve the following IBVP: u,(x, t) ="-(x,t) + (t-1)sin(m), 0
Suppose a system is governed by the following differential equation. Linearize this system about 0 0 radians, radians a. b. 4 Tt radians C. = (t) sin(0(t))u(t) CD
Suppose a system is governed by the following differential equation. Linearize this system about 0 0 radians, radians a. b. 4 Tt radians C. = (t) sin(0(t))u(t) CD
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:
4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u (x, 0) ura' (a, t) + 2t sin (2na:) , 0 < x < 1, 0, u(1,t)=0, t > 0, sin(2π.r)-5 sin (4π.r) , 0 < x < 1. t > 0, = = =
4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u (x, 0) ura' (a, t)...
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0<x <c,0 11 (c, 1) = 0, u(x, 0) = f(x), where u is continuous for0sxc,0 and where n is a positive integer. Answer: u(x, 1) Σ A,Jn(gjx) exp (-α,1), where a", and A, are the constants j-1
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0
Solve the given initial-value problem. dax + 4x = -7 sin(2t) + 6 cos(2t), x(0) = -1, x'(0) = 1 xce) = -cos(2+) – sin(2t) + {cos(21) + (sin(21) Need Help? Read It Watch It Talk to a Tutor
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