SOLUTION:
NOW WE DIVIDE THE GIVEN EQUATION WITH X THEN WE GET THE EQUATIONS AS
NOW SOLVATION GOES AS:
Q2. Consider the equation (a) [2 marks] Find the characteristics of the equation. (b) [4 Marks] S...
02 Comsider the linca ecomd order partia i (a) [2 marks] determine the class of the equation (b) [2 marks] Find the characteristics of the equation. 12 Marks] Sketch the characteristics in the (x, y) plane (c) (d) [2 Marks] determine the characteristic coordinates (e) [9 marks] Reduce the equation to standard form (f) [3 marks] find its general solution. 02 Comsider the linca ecomd order partia i (a) [2 marks] determine the class of the equation (b) [2 marks]...
Q1. Consider the equation (a) Find the characteristics of the equation (2). (b) R educe the equation to standard form and find its general solution (c) Use the general solution to find ux, y), if it exists, for each of the following Cauchy data: (iii) u(x,y)-- on the curve 0(2) y n(x,y)-2e-y On the curve 1 x Q1. Consider the equation (a) Find the characteristics of the equation (2). (b) R educe the equation to standard form and find its...
MATH4474: Introduction to Partial Differential Equations Revision Exercises chapter 2, 4-6 Q1. Consider the linear second order partial differential equation (i) (ii) (iii) Determine the class of this equation Find the characteristic coordinates Reduce the equation to canonical form 02. Consider the linear second order partial differential equation (a) [2 marks] determine the class of the equation (b) [2 marks] Find the characteristics of the equation. (c) 12 Marks] Sketch the characteristics in the (x, y) plane (d) [2 Marks]...
(10') Consider the equation Cut #cut = 1, 2 & R. (a) Find the characteristic curves. Sketch two curves on the t-x plane. (b) Define the characteristic coordinates. (c) Solve the equation with initial condition u(x,0) = x2 + 1.
Consider the partial differential equation, with the initial condition: 1 2 cup +3cºu, = 9x²y?, u(x,0) = x3 +1 Find the characteristic curves and the orthogonal trajectories and sketch both on the same graph. Find a solution of the partial differential equation with the given initial con- dition valid in the first quadrant of the (x, y)-plane. Is this solution unique? Explain.
Consider the following differential equation. (x2 − 4) dy dx + 4y = (x + 2)2 Consider the following differential equation. dy (x2 - 4) dx + 4y = (x + 2)2 Find the coefficient function P(x) when the given differential equation is written in the standard form dy dx + P(x)y = f(x). 4 P(x) = (x2 – 4) Find the integrating factor for the differential equation. SP(x) dx 1 Find the general solution of the given differential equation....
1. 2. 3. 4. (1 point) Eliminate the parametert to find a Cartesian equation for I=+2 y= 10 + 2t 2 = Ay? + By+C where A= and B = and C = (1 point) Consider the parametric curve: 2 = 8 sin 0, y = 8 cos 0, 0<<A The curve is (part of) a circle and the cartesian equation has the form 2? + y2 = R2 with R= The initial point has coordinates: 3 = !!! ,y=...
34. Consider a two-dimensional Cartesian coordinate system and a two-dimensional uv-system with the coordinates related by y = (1/2)(112-U2). In general, Laplace's equation in two dimensions can be written as with ох ду Zi (a) In the xy-plane, sketch lines of constant u and constant v. (b) Express Laplace's equation using the uw-coordinates. (c) Use the method of separation of variables to separate Laplace's equation in the v-system and obtain the general solution for ų'(u, u). 34. Consider a two-dimensional...
please answer question 1) to 3) fully step by step 7 marks (4 marks) (3 marks) (a) Is the operator P(v) y'+2ty linear? (Show workings) (b) Find the null space of the operator in (a) above. Question 2 5 marks Let P be a linear operator. Suppose that y is a particular solution to the equation Ply) = b. Prove that any solution to this equation can be written as y = Yo + yi for yo au clement of...
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation by H(s) a) D, and find the transfer function for the system above. (5 marks) Sketch the Bode plot. b) (5 marks) 4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation...