Question

In: Math

[2 marks] Suppose that the characteristic polynomial of the following Cauchy-Euler equation x2 y′′ + αx ...

[2 marks] Suppose that the characteristic polynomial of the following Cauchy-Euler equation

x2y′′ + αx y + βy  =  0

has roots m1  =  2 − 3i, and m2  =  2 + 3i. Find α and β.

Enter the values of α and β (in that order) into the answer box below, separated with a comma.

Solutions

Expert Solution


Related Solutions

find the general solution of the equation using cauchy euler. show complete solution x^2 y" -...
find the general solution of the equation using cauchy euler. show complete solution x^2 y" - 3xy' + 3y = 2x^4 e^x
D^2 (D + 1)y(t)= (D^2 +2)f(t) a.) Find the characteristic polynomial, characteristic equation, characteristic roots, and...
D^2 (D + 1)y(t)= (D^2 +2)f(t) a.) Find the characteristic polynomial, characteristic equation, characteristic roots, and characteristic modes of the system. b.) Find y_o(t), the zero-input component of response y(t) for t>=0, if the the initial conditions are   y_0 (0) = 4, y_0' (0) = 3, and y_0'' (0) = -1
For the following Cauchy-Euler equation, find two solutions of the homogeneous equation and then use variation...
For the following Cauchy-Euler equation, find two solutions of the homogeneous equation and then use variation of parameters to find xp. Before solving for xp you need to divide the equation by t2 to have the correct forcing function f(t). t2x'' − 2tx' + 2x = 8t xp =__________________
Consider a Cauchy-Euler equation x^2y''- xy' +y =x^3 for x>0. a) Rewrite the equation as constant-...
Consider a Cauchy-Euler equation x^2y''- xy' +y =x^3 for x>0. a) Rewrite the equation as constant- coefficeint equation by substituting x = e^t. b) Solve it when x(1)=0, x'(1)=1.
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation...
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy/dt and ypp for d2y/dt2.) x2y'' − 3xy' + 13y = 2 + 3x
a) Solve the Cauchy-Euler equation: x^2y'' - xy' + y = x^3 b) Solve the initial-value...
a) Solve the Cauchy-Euler equation: x^2y'' - xy' + y = x^3 b) Solve the initial-value problem: y'' + y = sec^3(x); y(0) = 1, y'(0) =1/2
In Exercises 1-20, find a general solution of the Cauchy-Euler equation. (Assume x > 0). (x^(2))y''-5xy'+9y=0
In Exercises 1-20, find a general solution of the Cauchy-Euler equation. (Assume x > 0). (x^(2))y''-5xy'+9y=0
Solve the Cauchy-Euler equation x4y'''' - 4x2y'' + 8xy' - 8y = 12xlnx x > 0
Solve the Cauchy-Euler equation x4y'''' - 4x2y'' + 8xy' - 8y = 12xlnx x > 0
t2 (d2r/dt2) - 9t (dr/dt) + 16r = 4 is an example of a "Cauchy-Euler equation."...
t2 (d2r/dt2) - 9t (dr/dt) + 16r = 4 is an example of a "Cauchy-Euler equation." Such equations appear in a number of physics and engineering applications. a) Write the complementary homogeneous equation. b) Plug r = ekt into the equation you wrote in part a. Show that this solution will not work for any constant k: this equation has no exponential solution. c) Plug the guess r = tn (where n is a constant) into the equation you wrote...
1. Suppose that the regression equation y = 16.99 + 0.32 x1 + 0.41 x2 +...
1. Suppose that the regression equation y = 16.99 + 0.32 x1 + 0.41 x2 + 5.31 x3 predicts an adult’s height (y) given the individual’s mother’s height (x1), his or her father’s height (x2), and whether the individual is male (x3 = 1) or female (x3 = 0). All heights are measured in inches. In this equation, the coefficient of ______ means that ______. x2; if two individuals have fathers whose heights differ by 1 inch, then the individuals’...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT