In a grid of wires, the temperature at exterior mesh points is maintained at constant values as shown in the figure. When the grid is in thermal equilibrium, the temperature at each interior mesh point is the average of the temperatures at the four adjacent points. For instance, T1=(T2+T3+0−10)/4. Find the temperatures T1, T2, T3, & T4, when the grid is in thermal equilibrium.

Q: Solve the homogeneous linear system corresponding to the parameters t and s.) 1001 0 0 1 0 0 0 0 0…

A: The given matrix is                                        100100100000

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A: First we will find complimentary solution (solution of homogeneous part) then using the method of…

Q: Find the particular solution that satisfies the initial condition. x3y'+2y=e1/x^2, y(1)=e

A:

Q: The metal plate has the constant te m­peratures shown on its boundaries. Find the equilibrium…

A: There are 4 interior and each adjacent to 4 other points.

Q: • Determine the particular solution given the general solution y(x) = c,e3x + cze-* and the boundary…

A:

Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 6y = 3e t %3D Y(t) =|

A:

Q: Find the general solution of 9y ′′ (t) + 12y ′ (t) + 32y (t) = t + et

A:

Q: Given: y = c, e2x +c C ze³r Find a solution of the second order IVP with y(0)=4 and y'(0)= -1 When…

A:

Q: HW/ solve the simultaneous D.Es. using L.T. y'+z =t, z'+4y = 0, y(0) = 1, z(0) =-I,

A:

Q: Find C1, C2, and Ca so that the given functions will satisfy the prescribed initial conditions. 4a.…

A: We will find out the required values.

Q: 2. Use the method of variation of parameter to solve the nonhomogeneous system X' = AX + F(t) where,…

A: X1=AX+F(t)A=1232    F(t)=2te2tThe characteristic equation of…

Q: The solution of the IVP t(t + 4)y + (t + 4) y= t, y(2) =2 exists in the interval

A: In the question it is asked to solve the initial value problem as shown below. t(t+4)y'+(t+4)y=t2…

Q: Given that y = e is a solution of the equation, ty" + (3t – 1)y + (2t – 1)y = 0, t>0 find a second…

A:

Q: Use variation of parameters to find the particular solution to 3t y'' + 5y + 4y = 2e Y(t)=| Preview

A:

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A:

Q: Use the graphical method to find all solutions of the system of equations, rounded to two decimal…

A: Given y=ex+e-xy=5-x2

Q: Use the method of reduction of order to find a second solution to t’y'" + 2ty' – 2y = 0, t > 0 Given…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Exercise 3 By using the method of undetermined coefficients, the particular solution of tje DE y6) +…

A:

Q: Find the general solution to t²y + (t + 1) y =t', for t > 0.

A:

Q: 3. A predator-prey interaction is given by AP = rP(1 – P) – PQ AQ = uQ(1– Q) +PQ. where r and u are…

A: A predator- prey interaction is given by △P=rP1-P-r2PQ △Q=uQ1-Q+u2PQ where r and u are positive real…

Q: Find the valye of m for y=e^mx to be a solution of y'-4y=0

A: As we know that the chain rule. fgx'=f'gx·g'x   From the given problem: y=emx.....1Andy'-4y=0...(2

Q: Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) +…

A:

Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system dx = 5x + 9y +…

A: Given system of differential equation is dxdt=5x+9y+7dydt=−x+11y+21 Write the given system of…

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A:

Q: Use the method of variation of parameters to find the general solution of the following DE.…

A: We will find out the required general solution for given differential equation using variation of…

Q: Find the temperatures T1, T2, and T3 when the grid is in thermal equilibrium. 0° 200° 0° T1 0° 200°…

A: When the grid is in thermal equilibrium, the temperature at each interior mesh point is the average…

Q: Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) +…

A:

Q: Q3. Given that y, - -3r²e¬#, y2 = 7x" are solutions of a linear homogeneous equation with constant…

A: We have to find the minimal order of equations.

Q: first finding particular intergral and complimentary solution.

A:

Q: Find C1, C2, and C3 so that the given functions will satisfy the prescribed initial conditions. 4a.…

A:

Q: Find the values of c, and c2 so that the given functions will satisfy the prescribed initial…

A:

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A: Introduction: one or more derivatives of a function are included in an equation. Equations involving…

Q: Find the value of y, for wich the solution of the I.V.P y' - y =1+3sin t, y(0) = yo remains finite…

A: Here we are given an I.V.P                                         y'-y=1+3sint Also it is given…

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A: Given

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A:

Q: ťy" – t(t+ 2)y' + (t+2)y = 0, t > 0.

A:

Q: Given that y, =t2 is a solution to the DE ty" - 3ty' + 4y = 0 on (0, o0), use reducti econd…

A:

Q: The function U(x, y) satisfies the equation a²U_a?U + ax2 ' ay2 = -2, at every point inside the…

A:

Q: For the system X"(t) = A(t).X(t)+ B(t),X(0) = 0 where 1 e' e' e' A(t) = e e' 0| and B(t) =| e'|…

A: The largest interval containing t=0 at where every element function are continuous.

Q: Determine C, and C, so that y(x) = C¸ e²* + C2e* + 2sinx will satisfy the conditions y(0) = and…

A: Put x=0 in y(x).

Q: H. W : Perform three iterations to approximate a root of the system described by fi(x, y) = x2 - xy…

A:

Q: 10. Using 5x5 grids, determine the equation for steady state temperature distribution at T21, T22…

A:

Q: Q3/ Determine the solution of a?u du arz subject to boundary conditions u(0,t)= u(2,t) = 0 %3D at…

A: Given pde is heat equation. Solution of this pde given by

Q: Sketch an approximate solution curve that passes through each of the indicated points

A: Here is the solution of the given problem.

Q: Find the value(s) of m such that the function y=e^(mx)is a solution of the DE 2y"+7y'-4y=0

A: Find the value(s) of m such that the function y=e^(mx)is a solution of the DE 2y"+7y'-4y=0

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A:

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y(-)= 3x²y² becomes A none…

A: We have to write the differential equation in terms of dz/dx.

Q: Use the method of undetermined coefficients to determine only the form of a particular solution for…

A:

Q: Use the method of undetermined coefficients to find a general solution to the system x' (t) = Ax(t)…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.