Solve the following non-homogeneous differential equations: x" (t) + x(t) = 2 cost 1) -X 2) y"+2y+y = xe 3) x²y"-2xy'+2y = x lnx (Hint: by change of variable, let x=e¹)

Q: .SS. Write an iterated integral for dA over the region R described to the right R using a. vertical…

A:

Q: What is the unit tangent vector T(t) on the curve r(t) = (sin(t), 3, 2 cos (2t)) when t = 0? Select…

A:

Q: (2) Solve the given homogeneous equation by the appropriate substitution y dx (x + y) dy = 0. - You…

A:

Q: Consider the function graphed to the right. Make sure to use the union symbol, U if needed. The…

A:

Q: A company that manufactures pet toys calculates that its costs and revenue can be modeled by the…

A:

Q: (a) Find and sketch the domain of the function f(x,y)=√x-1+√y-4

A:

Q: 8. Consider the gradph of the function f(x, y) = x² - 5xy given by z = x² - 5xy (a) ( (1,2). Find an…

A:

Q: Sketch the region of integration of 2 So Soft + S₁² √ √² Then evaluate the integral by first…

A:

Q: Find the volume of the region under the surface z = xy² and above the area bounded by x = y² and x +…

A:

Q: (Order your answers so the x-coordinates are in order from least to greatest.) f has ---Select---…

A:

Q: True or false: Suppose that a is a real number. The graph of y = f(x) has a vertical asymptote at x…

A:

Q: Find the inverse matrix where A = 1 -1 2 -3 -3 1 2 -3 -3

A:

Q: An employee's monthly productivity M, in number of units produced, is found to be a function of the…

A: An employee's monthly productivity M, in number of units produced, is found to be  a function of…

Q: A golf ball manufacturer knows the cost associated with various hourly production levels, given…

A: Production cost for golf balls is given as,

Q: Help determine the difference quotient and for f(x)=x^2+4

A: Given,. Difference quotient=

Q: = O Trigonometric Identities and Equations Proving an identity using fundamental trigonometric…

A: 1+tan2x

Q: Consider the function f(x) = { 4x² =−x+5c_if x ≤ 2 - 4x if x > 2 For what value of c is the function…

A: given function

Q: Find the general solution of the first-order linear equation dy dx + 2y = e²x

A:

Q: Z₁ cos# = 2 V₁ 1 V +(x-2- sin e Z₁ cos Z₁ X + V₂ V₂ cos 9) +1/+ Z₁ 1 V. cose V 2 -sin 0 +

A:

Q: A school wishes to form three sides of a rectangular playground using 240 meters of fencing. The…

A: A school wishes to form three sides of a rectangular playground using 240 meters of fencing. The…

Q: Find the area of the shaded region. y 3 2 1 (1, 1) 2 y = ³x y || 4 1 X 6 X = 8 CO 8 X

A: Given equations of the curve

Q: Given C = x³ – 6x² + 9x +4 13 a) Find C'(x) = Find any critical values of C'(x) b)x= Use interval…

A: Given,

Q: If f(t) = (t² + 3t+2) (5t² + 4), find f'(t). 201³ + 45t² + 32t Find f'(2). 40 X

A:

Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

A:

Q: Find for the following: (a) xy = cot(xy) dy dx (b) x²y = y

A: To find  for the following: (a) (b)

Q: Determine the function f satisfying the given conditions. f ''' (x) = 12 f '' (0) = 1 f ' (0) = 2 f…

A: Given that Let

Q: A piece of cardboard measuring 11 inches by 14 inches is formed into an open-top box by cutting…

A:

Q: Step 3 Write the two binomial factors so that the first term of each factor is x and the second…

A: To write the complete factorization of

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: The function is given byTo determine: The absolute maximum and minimum values of the function.The…

Q: A formula for the derivative of a function f is given. How many critical numbers does f have? f'(x)…

A: The critical number refers to the value at which the first derivative f' (x) of the real valued…

Q: Answer the following questions for the function f(x)=x√x² + 36 defined on the interval -4 ≤ x ≤7.…

A:

Q: Evaluate the following integral, f (x - 5y) dx - 8y² dy where C' is given by x = y² + 6 from (7, 1)…

A:

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: The given integral..We have to find the solution to the integral.Formulas used:

Q: Given the following integral and value of n, approximate the following integral using the methods…

A:

Q: Find the lines that are tangent to the curve y = 2tan(pi*x/4) at x=1

A: The equation of tangent line passes through point  with slope

Q: What is the center of the sphere given by the equation x² - · 6x + y² – 2y + z² +82 +17 = 0? -…

A: The standard equation of a sphere is given by  where (h,k,l) is the center of the sphere and r is…

Q: r(t) = 2t²1 - 4tj + 2t³k (a) r(t) (b) r"(t) (c) r(t)r"(t) (d) r(t) x r"(t)

A:

Q: Find the horizontal and vertical asymptotes of f(x). 2x² f(x)= Find the horizontal asymptotes.…

A:

Q: Use a linear approximation (or differentials) to estimate the given number sqrt(99.2)

A: SolutionLet f(x)=√x and use the linearization at a=100

Q: Use a graphing calculator or computer to verify the given linear approximation at a = 0. Then…

A: The given function is

Q: Consider the following differential equation to be solved by the method of undetermined…

A:

Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) =x² + y² subject to the…

A:

Q: Find the solution of the following problem. y' - (x + y)(x + y +3) = 1

A:

Q: Let f(x) = 3x + 3 and g(x) = −3x - 7. Compute the following. (a) (fog)(x) (b) (fog)(8) (c) (gof)(x)…

A:

Q: Given that (fog)(x)=x-8, which are correct rules for f(x) and g(x) that result in this composite…

A:

Q: The table below gives the velocity of a runner at half- second intervals during the first three…

A: Given the table below gives the velocity of a runner at half-second intervals during the first three…

Q: Use Substitution method 4x - 3y = 5 x + 2y = 4

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find aw/as and aw/ât using the appropriate Chain Rule. Function Values w = y³ - 2x²y x = es, y = et…

A:

Q: What is the volume if a 6 inch square is cut out

A: Consider the box

Q: For which values of x are the vectors (2x, 4, x) and (-1, -2, x) orthogonal? Select one: O-4 and 2…

A: