2. Find the derivative of +e= e. State the solution in the form , where a...
2. Using the method of Frobenius, find the general solution about the point i = 0 of the ordinary differential equation 1 (1 - 4) y" - ry' +y = 0. Simplify your answer as much as possible and state the domain of validity. 110 3. Consider the general series solution about the point I = 0 of the ordinary differential equation e'y' + 2y = 0. Find the coefficients of all the terms of this series solution up to...
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e the equation so that it is in form 1, if possible. If it is not possible to put it in form 1, then put it in form 2, and find ef P()dx form 1: vvdy w(x)dx form 2: dx +Poy-) The symbols a, b and c are nonzero constants Your final answer must have like terms combined and fractions reduced. Also, your final answer is to have as few exponents as possible. (An exponent that has...
12. For the following function find the derivative, factor and simplify and find where the tangent is horizontal: [6 marks)
d. Find the general solution of the differential equation56-48x + 49y - 42xy dx Give an implicit solution in the form F(x)GK, in which the coefficient of x2 is 84. Answer: =K e. Find the particular solution of the differential equation (4 +x2)으-2V 16-r, such that y-t as x →-2. dx Simplify your answer as much as possible. Answer: y=
d. Find the general solution of the differential equation56-48x + 49y - 42xy dx Give an implicit solution in the...
a) Evaluate the Eigenvalues and Eigenvectors of matrix A. b) Evaluate State Transition Matrix e Al using only the method of Cayley-Hamilton, et = Bol + B1A. Clearly indicate what B, and B1 are and simplify the result as much as possible. Simplify eAt as much as possible. A = []? -
Consider the ODE:3xy"+y' - 2xy = 0. Find the general solution in power series form about the regular singular point x = 0, following parts (a) – (c), below. (a) Obtain the recurrence relation. (b) Find the exponents of the singularity. (e) Obtain only one of the two linearly independent solutions, call it y(x), that corresponds to the smaller exponent of the singularity; but, only explicitly include the first four non-zero terms of the power series solution. Write down the...
Question 2 of 14 (1 point) Differentiate the given function. The derivative of the function is f(x)- 1 Express your answer with positive exponents only
Problem 4 Let V be the vector space of functions of the form f(x) = e-xp(x), where p(x) is a polynomial of degree (a) Find the matrix of the derivative operator D = d/dx : V → V in the basis ek = e-xXk/k!, k = 0, 1, . .. , n, of V. (b) Find the characteristic polynomial of D. (c) Find the minimal polynomial of D n.
Problem 4 Let V be the vector space of functions of...
(1 point) Let y" + ly' – 12y=0. a. Try a solution of the form y=e", for some unknown constant r, by substituting it into the differential equation. = 0. help (formulas) b. Simplify and factor your equation in the previous part as much as possible. Be sure to divide out any factors guaranteed to be nonzero. = 0. help (formulas) c. Find all values of r such that y=e" satisfies the differential equation. If there is more than one...
Write the equation in exponential form. 1 log =-2 100 The equation in exponential form is Write the equation in logarithmic form. 10º = 1,000,000,000 The equation in logarithmic form is Simplify the expression. log 0.0001 = Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possibl Assume that the variables represent positive real numbers. Vab In Write the logarithm as a sum or difference of logarithms. Simplify each term as much as...