Chapter 3, Section 3.2, Question 01 Find the Wronskian of the functions f (t) = e5t...
Chapter 3, Section 3.2, Question 009 Find the derivative of the given function. y = + 8 Vx Enclose arguments of functions, numerators, and denominators in parentheses. For example, sin (2x) or (a - b)/(1 + n).
Chapter 3, Section 3.5, Question 12 Find the solution of the given initial value problem. 01 -25 x(0)= 10) x, Click here to enter or edit your answer The solution is given by x(t) -
Chapter 6, Section 6.2, Question 04 Find the inverse Laplace transform --1{F(s)} of the given function. 6s+36 FS) $2+12s+100 Your answer should be a function of t. Enclose arguments of functions in parentheses. For example, sin (22). -1{F (3)} = QC
Recall: Given two functions f(t) and g(t), which are differentiable on an interval I, • If the Wronskian W(8,9)(to) #0 for some to E I, then f and g are linearly independent for all te I. • If f(t) and g(t) are linearly dependent on I, then W (8,9)(t) = 0 for allt € 1. Note: This does NOT say that "If W(8,9)(x) = 0, then f(x) and g(2) are linearly dependent. Problem 2 Determine if the following functions are...
TIMER Chapter 6, Section 6.1, Question 01 Determine whether f is continuous, piecewise continuous, or neither on the interval Osts 3. (2+² Ostsi f(t) = 5+t, 1<ts2 9-t, 2 <ts 3 piecewise continuous neither continuous
Chapter 3, Section 3.2, Question 07 (a) State whether the given system is autonomous or nonautonomous and also whether it is homogeneous or nonhomogeneous. x' x+y11, y = -31x+ sin (t) y The given system is (b) Write the system using matrix notation. ()-) = P +g where [Enter as 2x2 matrix.] P = [Enter as 2x1 matrix. g Chapter 3, Section 3.2, Question 07 (a) State whether the given system is autonomous or nonautonomous and also whether it is...
Chapter 6, Section 6.1, Problem 01 Which of the functions sketched below could be a probability density function for a continuous random variable? 式2) 0.5 0 (i Your answers (a) f 7 be a probability density function (b) f be a probability density function (c) f ▼J be a probability density function (d) f ▼-be a probability density function
Chapter 3, Section 3.2, Question 017-018 For the function f (x) = a(x – r) (x – s) graphed below, state whether the constants a, r, and s are positive, negative, or zero. (Assume r < s.) a is ris s is 4. . . sis
Chapter 6, Section 6.2, Question 04 x Your answer is incorrect. Try again. Find the inverse Laplace transform L {F(s)} of the given function. 2s +12 F(S) = 2+12s+45 Your answer should be a function of t. Enclose arguments of functions in parentheses. For example, sin (2c). 2-'{F(s)} = 2e^(-3t)cos(6)
gnment Chapter 5, Section 5.6, Question 01 Consider the following differential equation. (a) Find all the regular singular points of the given differential equation If necessary, enter your answers separated by commas. page (b) Determine the indicial equation and the exponents at the singularity of each regular singular point Enter the values of ri and r2 in increasing order F(r)- ак a t