Consider the differential equation below.
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Consider the differential equation below.
Consider the differential equation (a) Take the Fourier transform of this differential equation to show that where y(k) is the Fourier transform of y(x). (b) Hence calculate y()
Consider the differential equation (a) Take the Fourier transform of this differential equation to show that where y(k) is the Fourier transform of y(x). (b) Hence calculate y()
2. Consider the following partial differential equation (a) Separate this equation into two ordinary differential equations (b) Translate the following boundary conditions on the above partial differential equation to conditions on the ordinary differential equations found above.
2. Consider the following partial differential equation (a) Separate this equation into two ordinary differential equations (b) Translate the following boundary conditions on the above partial differential equation to conditions on the ordinary differential equations found above.
Consider the differential equations The slope field depicted below corresponds to one of these Which differential equation matches the direction field?
e-2 is a 0. Given the fact that y= e' 1. Consider the differential equation y" + 4/" +14y' +20y solution of this differential equation, answer the questions below. [5 ptsl(a) Find a basis for the solution space of this differential equation.
3. Consider the following differential equation 0o and a series solution to the differential equation of the form a" n-0 (a) Find the recurrence relations for the coefficients of the power series. 3 marks] (b) Determine the radius of convergence of the power series. l mar (c) Write the first eight terms of the series solution with the coefficients written in terms of ao and ai 2 marks]
3. Consider the following differential equation 0o and a series solution to...
Consider the differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation above. T1,T2 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. n(t) = v2(t) (c) Find a particular solution yp of the differential equation above. Bplt)
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....
dy 3. (5 points): Consider the autonomous differential equation dt is given below. Draw the phase line and classify the equilibria. f(y) where the graph of f(y) Y 1 -0.5 0.5 1 y
Consider the following differential equation to be solved by variation of parameters. y'' + y = csc(x) Find the complementary function of the differential equation. yc(x) = Find the general solution of the differential equation. y(x) =