Find the Legendre’s polynomial ??(?) from the differential equation (1 − ?2) ?2?/??2 − 2? ??/??...

Find the Legendre’s polynomial ??(?) from the differential equation (1 − ?²) ?²?/??² − 2? ??/?? + 6? = 0 and represent the Legendre’s polynomial with equation.

Expert Solution

Colby Messinger answered 1 week ago

1. What is a differential? 2. What is a differential equation?

1. What is a differential? 2. What is a differential equation? 3. Besides the fact that you might need the course to graduate, how might differential equations be useful to you in real life?

Consider a nonhomogeneous differential equation ?′′ + 2?′ + ? = 2? sin? (a) Find any...

Consider a nonhomogeneous differential equation ?′′ + 2?′ + ? = 2? sin? (a) Find any particular solution ?? by using the method of undetermined coefficients. (b) Find the general solution. (c) Find the particular solution if ?(0) = 0 and ?′(0) = 0.

Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where...

Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where x=[x(t)y(t)]. x(t)= y(t)= please be as clear as possible especially when solving for c1 and c2 that's the part i need help the most

1. (a) Sketch the slope field for the given differential equation: dy/dx = 2? (b) Find...

1. (a) Sketch the slope field for the given differential equation: dy/dx = 2? (b) Find the particular solution of the differential equation that satisfies the initial condition y(0) = 4 (c) What is the value of y when x = 1/2 2. (a) Find the general solution of the given differential equation: dy/dx = ysinx = ????? 2 (b) Find the particular solution of the differential equation that satisfies the initial condition ? = 2; ?ℎ?? ? = π/2

1.) Let f′(x) = 3x^2 − 8x. Find a particular solution that satisfies the differential equation...

1.) Let f′(x) = 3x^2 − 8x. Find a particular solution that satisfies the differential equation and the initial condition f(1) = 12. 2.) An object moving on a line has a velocity given by v(t) = 3t^2 −4t+6. At time t = 1 the object’s position is s(1) = 2. Find s(t), the object’s position at any time t.

Polynomial Equation

Write a polynomial equation that has -6 and 4 as solutions.

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

Question

Find the Legendre’s polynomial ??(?) from the differential equation (1 − ?2) ?2?/??2 − 2? ??/??...

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