You have been given the following equation. It is a non-homogeneous differential equation. y" + 81y = sec²(9x) Assuming that c1 and c2 are arbitrary constants. The general solution to the related homogeneous differential equation of: y"+81y=0 is the function: yh(x) = C1y1(x) + C2y2(x) = C1_ Assuming yp(x) is the particular solution to the differential equation: y" + 81y = sec²(9x). yp(x) is of the form yp(x) = y1(x)u1(x) + y2(x)u2(x) where; u'1(x) = & u2(x) = It follows that u1(x) = And thus yp(x) = Knowing this, the most generalized solution to the non-homogeneous differential equation y" + 81y = sec (9x) Would be: y = C1 & u2(x) = + C2

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(x) = √√₁²₁1 + 1² dt 1…

A:

Q: A particle moves along a line so that, at time t, its position is s(t) = 6 sin(7), t20. What is the…

A:

Q: Sketch the region R and evaluate the iterated integral y 2.0 1.5 1.0 0.5 1-2x+By) dy dx " ((x, y)…

A: The given integral is

Q: Evaluate the integral using the following values. [x³ dx = 260, fºx dx -10, [ºdx=2 (x-16 - 16) dx

A:

Q: 10 of the - dx is 1 x² The value of

A:

Q: Calculate the velocity and acceleration vectors and the speed of r(t) = ( 82², 8+2²) at the time t =…

A:

Q: Use a triple integral to find the volume of the solid bo Z= = 3x², y = 6 - 6x, first octant JO JO dz…

A: Given thatNow, In first octant all variables are bounded by .we can bound the variable x using…

Q: Determine if the improper integral is convergent or divergent, and calculate its value if it is…

A:

Q: Use the given transformation to evaluate the given integral, where R is the region bounded by the…

A:

Q: Find the minimum and maximum values of the function y = 12t³ + 18t² on [1, 2] by comparing values at…

A:

Q: Given f(x) dx = 17 and (a) (b) (c) (d) L₁ (r(x) [f(x) + g(x)] dx g(x) dx = -5, evaluate the…

A: Given definite integral values

Q: 4. Consider the function f(x)=x², x > 0. (a) Determine limo+ f (x). Hint: First use L'Hospital's…

A:

Q: Let f(x) = +15 Find the critical points e that correspond to local minima. (Use symbolic notation…

A: Note : As per our Guidelines , we will solve first three subparts as your all subparts are not small…

Q: Use linear approximation, i.e. the tangent line, to approximate 8.3 as follows: Let f(x)=x. The…

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Determine whether the sequence an= 5n+3 Justify your answer. is monotonic. Is it bounded?

A:

Q: Find the critical points c for the function ƒ and apply the Second Derivative Test (if possible) to…

A:

Q: 2) Sketch a graph that has all of the following properties: zeros at x = 2,-4 y-intercept at (0,2)…

A: To sketch a graph of function with given properties

Q: Find a vector-valued function whose graph is the indicated surface. The plane z = 3y r(u, v) =

A: Given  plane       Let's make substitution Hence  we get

Q: A particle moves in a straight line with velocity 12 - 4t ft/s. Find the total displacement and…

A:

Q: 2 Cost function (y₁ - (mx₂ +b)) + m² + b² 1 & b with respect pect to d cost function dm & cost…

A:

Q: Evaluate the iterated integral. 18 ԱՐ: 8ze 18 dy dx dz

A:

Q: Connecting the Communication Device With the communication device pointed toward your home planet,…

A: In this question , we will solve the derivative of the given function at some value and rearrange .

Q: The figure is the graph of the derivative, f', of a function f on [-4,4]. AA Determine the intervals…

A:

Q: Find the radius and interval of convergence for the following series: (x − 1)” n³3n a. n=1 Radius=…

A:

Q: Be sure to show and explain all steps. Determine lim X→C 2f(x) - 3h(x) (g(x))+ (h(x))* lim _f(x) = 8…

A:

Q: The daily cost per unit of producing a product by the Ace Company is 5 + 0.5x dollars and the price…

A: Daily cost per unit of product a produced by the Ace Company = 5 + 0.5x dollars.The price in the…

Q: y £= + 1 2 34 Graph of f The figure above shows the graph of function f with domain 0 ≤x≤ 4. Which…

A: Graph of f :

Q: Use the graph off to complete parts (a) through (1). If a limit does not exist, explain why. 8- Ау…

A:

Q: Find F'(x). F'(x) = F(x) = x + 5 [**5 X (4t + 9) dt

A: To find .

Q: Write the equation of the line tangent to the graph of the function at the indicated point. As a…

A:

Q: Find the volume of the solid fromed by rotating the region enclosed by x=0, y=0, ×=1, y=5+x^2 about…

A:

Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

A:

Q: The region D above lies between the graphs of 1 y = −3 − (x + 4)² and y = −7+ (x +6)³. It can be…

A:

Q: Find the accumulated present value of a continuous stream of income at rate R(t) = $136,000, for…

A:

Q: Rewrite sin (x +7) 7) in terms of sin æ and cos æ. 6 Enclose arguments of functions in parentheses.…

A:

Q: The traffic flow rate past a certain point on a highway is q(t) = 1500 +2400t - 360t² where t is in…

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) so (70 - 3 csc(0)…

A:

Q: Calculate the left Riemann sum for the given function over the given interval using the given value…

A: To calculate the left Riemann sum for the given function over the interval [−2, 2] using n = 4 and…

Q: a. x = 2y, y = 2 and y= 3; revolved about x-axis 4. (0, 3) y=3 (0, 2 y=2 -2. -4. 0 x=0 x = 2y + 2.…

A:

Q: Evaluate the integral using the following values. 8 8 [²x-360. [xx-24. [dx-s = 4 x³ dx = 960, dx dx…

A: given the values of integrals

Q: Find the average of the function over the given interval. f(x) = x3 − x over [0, 1]

A: The given function is

Q: Over what interval is the reciprocal of this function decreasing? Oa) {x R x ≤ -1} E Ob) { ER x -1}

A:

Q: A population P obeys the logistic model. It satisfies the equation dP 6 -P(7 - P) for P >0. dt 700…

A:

Q: A rectangular closed box is to be built at minimum cost to hold 729 cubic inches. Since the cost…

A: To find the dimensions that will minimize the surface area of the rectangular closed box, we'll use…

Q: passes directly over a tracking telescope on the ground. When the angle of elevation is x/3, this…

A:

Q: What statement is true about the function f(x)=e*+x? O A) It has an absolute maximum at x = 0 ○ B)…

A:

Q: Calculate the left Riemann sum for the given function over the given interval using the given value…

A:

Q: A car rental company charges 50 dollars per day, 15 cents per kilometre driven, and a 30 dollar…

A: Given query is to calculate the cost function.

Q: An object thrown vertically upward from the surface of a celestial body at a velocity of 18 m/s…

A:

Q: DEMAND FOR HYBRID CARS A car dealer determines that if gasoline-electric hybrid automobiles are sold…

A: Selling price of car: x dollars apiece, where Cost of gasoline: y cents per gallonFunction to…