Problem 10. Solve the following homogeneous systems 32 2 101 2. x'0 2 1 0 ж. 0 00 2 Problem 10. Solve the following homogeneous systems 32 2 101 2. x'0 2 1 0 ж. 0 00 2
Solve The Given Initial-Value Problem. The DE Is Homogeneous. (X + Yey/X) Dx ? Xey/X Dy = 0, Y(1) = 0
(1 point) Solve the heat problem with non-homogeneous boundary conditions du (x, 1) = ot (x,1), 0<x<2, t> 0 dx (0,t) = 0, (2, 1) = 2, t> 0, u(x,0) = 0<x<2. Recall that we find h(x), set u(x, t) = u(x, t)-h(x), solve a heat problem for u(x, t) and write u(x, t) = u(x, t) + h(x). Find h(x) h(x) = The solution u(x, t) can be written as u(x, t) = h(x) + u(x, t), where u(x,...
1. Solve the following homogeneous differential equation. ty' = 1. cos (6) + y 2. Solve the following Bernoulli differential equation 3. Solve the following initial value problem. (Hint: transform the equation to a separable equation through a substitution) y-(x + y + 1)? (0) - V3 - 1 4. Let T represent the temperature (in °F) of an object in a room whose temperature is kept at a constant 60°. If the object cools from 100 to 90° in...
3. Solve the following system of homogeneous equations 2.x1 + x2 + 3x3 = 0 x₂ + 2x2 x2 + x3
Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0 < t < oo 0 IC: u(z,0)= sin(nx)+x, 1 x by transforming it into homogeneous BCs and then solving the transformed problem
Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0
Solve the following homogeneous wave equation: un (2. t) = 4uxx(x, t), u(0.t) = u(t) = 0, u(x,0) = 0, (3,0) = 1.
Consider the following 2nd order nonhomogeneous linear equation
x 00 + 4x 0 + 5x = cos 2t
1. Solve for the fundamental solutions of its associated
homogeneous equation.
2. Find a particular solution of the nonhomogeneous
equation.
3. Based on your answer to the previous two questions, write
down the general solution of the nonhomogeneous equation.
Problem II (15 points) Consider the following 2nd order nonhomogeneous linear equation x" + 40' + 5x = cos 2t 1. (6 points)...
(10) 2. Solve the homogeneous equation by making the substitution y = xv y' x + 2y 2x + y' > 0.
(1 point) Solve the heat problem with non-homogeneous boundary conditions ди (x, t) at = a2u (2,t), 0 < x < 5, t> 0 ar2 u(0,t) = 0, u5,t) = 3, t>0, u(x,0) = **, 0<x< 5. Recall that we find h(x), set v(x, t) = u(x, t) – h(x), solve a heat problem for v(x, t) and write u(x, t) = v(x, t) +h(x). Find h(c) h(x) = The solution u(x, t) can be written as u(x,t) =h(x) +...
number 3 use variation of parameters for homogeneous linear
systems
02 1 2. X'= 1 1 -2 X 2 2 -1 1 2 0 3. X' = X+ 1 e tant 2