3. In the following questions, each part is independent. (a). Suppose that a 5-th order homogeneous linear differential equation with constant woefficients has characteristic roots li.e., the corresponding characteristic polynomial has the roots). - 2-3i, -2+3i, 5, 5 and -1. Find a general solution to this differential equation. x-2 are solutions to (b). Show that x² and x-² are x²y" + xy² - 4y = 0, where x >0 Find a general solution of this differential equation. reason why your solution is a general solution. Give a

3. In the following questions, each part is independent. (a). Suppose that a 5-th order homogeneous linear differential equation with constant woefficients has characteristic roots li.e., the corresponding characteristic polynomial has the roots). - 2-3i, -2+3i, 5, 5 and -1. Find a general solution to this differential equation. x-2 are solutions to (b). Show that x² and x-² are x²y" + xy² - 4y = 0, where x >0 Find a general solution of this differential equation. reason why your solution is a general solution. Give a

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The point x = 0 is a regular singular point of the differential equation. x² + (²x + x²) x² - y = 0. Use the general form of the indicial equation (14) in Section 6.3 r(r-1) +ar+b=0 (14) to find the indicial roots of the singularity. (List the indicial roots below as a comma-separated list.) r= Without solving, discuss the number of series solutions you would expect to find using the method of Frobenius. O Since these differ by an integer we expect to find two series solutions using the method of Frobenius. pong ini Since these do not differ by an integer we expect to find one series solution using the method of Frobenius. Since these differ by an integer we expect to find one series solution using the method of Frobenius. O Since these are equal we expect to find two series solutions using the method of Frobenius. O Since these do not differ by an integer we expect to find two series solutions using the method of Frobenius.
Obtain the differential equation by eliminating all arbitrary constants. 1.) y² = Ax² + B secx
Suppose tx1 + 2x2 + sec(t), sin(t)x1+ tx2 – 3. This system of linear differential equations can be put in the form æ' = P(t)æ + g(t). Determine P(t) and g(t). P(t) = g(t) =
Pls answer this :))
Reduce the following equation into its canonical form and find the solution in terms of two functions f and g: y202u əx² J²u дхду 2xy- +x20²u 1 ди Əx + dy² xy ду Note: You do not need to determine the function f and g but you need to find their arguments in order for the solution to satisfy the differential equation.
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