What is the general solution for the following differential equation? d²y dr² dy 4+y=0 dr Ⓒy=C₁e²-C₁₂e²² =ex (C₁₂cos.x + C₁₂sin x) y=e*(C_cosx +C_sin.x) Oy=C₁cos x + C₂sin x

Q: pref ย 8]T C {}},

A:

Q: Q15) The Parallel Postulate of Euclid is equivalent to: A) The Plane separation postulate B) Pasch's…

A: Solution

Q: a = 3i - 2j + 5k and b = -2i-j+k, find 2a-3b and also its unit vector.

A:

Q: 10. If x represents the solution set from the number line above, which of the following describes…

A: As per policy only first question is answered. The given is dark from x = -2  to x = 5.

Q: 4 1

A:

Q: Compute the length of the curve r(t) = (−4t, 4t + 3, −8t + 8) over the interval 0≤t≤7 L =

A:

Q: Solve the Differential Equations. 3.44 Test for homogeneity 3. f(x, y) tanx - sec²x - cosy

A: Let's find function is homogeneous or not.

Q: Complete the table below. Assume ƒ and g are one-to-one functions. x -10 6 g(x) (fog)(x) (gof)(x) 7…

A: We have to fill up the table

Q: Let A(z) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

A: Topic-Area bounded by curves

Q: Find the constant a such that the function is continuous on the entire real line. 9x², ax - 3, a = x…

A:

Q: f(x) (b) 1 x + 3 lim f(x) X-3+ -4 -2 2 -2 -4 2 X Determine whether f(x) approaches ∞ or -∞o as x…

A: This question is based on left hand limit and right hand limit.

Q: Find the following limits. √x-3 X-9 x-9 1. lim t²-7t+10 2. lim- t-2 t-2 3. A function f(x) satisfies…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: Given the integral from 0 to x of the function e-t^2dt: Find the summation form of its Maclaurin…

A: We know that: et=∑n=0∞tnn!⇒e-t2=∑n=0∞(-t2)nn!=∑n=0∞(-1)nt2nn!

Q: Q8. Let ABC be a triangle in the E.G. Assume E, F points on AB. AC respectively such that…

A:

Q: Find a parameterization for the curve shown in the figure below. r(t) where = -1 140 <t<

A: This equation can be solved by applying the concept of equation of line joining two points in two…

Q: 1. Determine the order of each of the following differential equations, and state whether it is…

A:

Q: if f(x) = x + 5*. find the derivative of this function f'( A. f'(x) = 5* In 5

A:

Q: Show the complete solutions. Family of circles centered at the line y = 2x. Ans: y" (y-2x) + 2(y')³…

A: To find out the differential equation for the family of circles having centre on the line y=2x.

Q: Calculate 127 y [1/10 ds where C is the parabola r(t) = (t, t², 0). Let 1 ≤ t ≤ 4. X

A:

Q: The parametric form of the tangent line to the image of f(t) = (2t², 3, t - 1) at t = 4 is t L(t) =

A:

Q: answer

A: As per policy only first question is answered. Please refer to the image below

Q: Eliminate the arbitrary constants in the equation defined by y = ae^(3x) + bxe^(3x). Which of the…

A:

Q: A bacteria culture starts with 600 bacteria and doubles in size every half hour. Exercise (a) How…

A:

Q: Change the following integral to polar coordinates and evaluate: 4-x² [2² 0 x² + y² dy dx Sketo

A: To convert Cartesian coordinates into polar coordinates we use the following transformation, x=rcosθ…

Q: Find the standard form of a circle given the following conditions. Sketch the graph. 1. Center at…

A:

Q: 2. Solve the Differential Equations. (y² - xy )dx + x² dy HO

A: To solve the given differential equation.

Q: 3. f(x,y) tanx - sec²x - cosy

A:

Q: 1.x*-4xy=c 2.y=C₁x+C₂e-4x Hint: multiply by ex

A:

Q: Solve the following integrals:- (2) S dx (1) Sx3-2x² dx x²√√9-x²

A: As per bartleby guidelines we only give first question answers.  Please repost for other parts.

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A:

Q: Iff (x) = f x² dx, what is f' (d)? Let a = 6 and d = 16.

A: Given that fx=∫axx2dx we have to find the value of f'd, for a=6 and d=16 use the formulas:…

Q: Use Part II of the Fundamental Theorem of Calculus to evaluate the integral. So (cx³ + dx² + e) dx…

A:

Q: Which of the following is the differential equation of the family of straight lines with slope "m"…

A:

Q: Evaluate each limit or state it does not exist a) lim 6x²-5x-1 x →1 2x² - x - 1 b). x²³_8 lim X-2…

A: a3 - b3 = (a-b)(a2+ab+b2)

Q: 2. dx tanx 4t² dt

A: To differentiate the given function.

Q: Q6. Let O(0,0), A(1,0), B(1,4) be points in the plane R². Then the following point lies in the…

A: I am attaching image so that you understand each and every step.

Q: Question Define R as the region bounded by the functions f(x) = e and g(x) == between x = 0 and x =…

A: To define R as the region bounded by the functions fx=ex2, and gx=x2, between x=0 and x=3. If R is…

Q: 1. Find if the function is continuous in the given points (sin(x+y) x+y 1 D) f(x, y) = x + y = 0…

A:

Q: Find the derivative of the vector function r(t) = ln(19 - t²)i + √17+tj − 7e-¹t k - r' (t) = (¯¯

A:

Q: The following image shows the graph of the function f(x)=√√4-x² A -2 B 6.27 square units 7.5 square…

A:

Q: Solve the differential equations 1. (3x²2y²)y' = 2xy 2. (y² - xy)dx + x²dy = 0

A:

Q: 1) Find the vertical, horizontal, and oblique asymptotes, if any, of f(x) = x²+1 x2-5x-14

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: I cos (x) sin(x) dx A. (sin²(x)) + C 2 B. (sin² (2x)) + C 2

A:

Q: if f(x) = %79.1 x²√In x² x -. find the derivative of this function f'(x) A. f'(x) = - 1 3:16 1-In x²…

A: The given function is; f(x)=x2 sqrt(ln x2)/x.

Q: SHOW YOUR SOLUTION: Solve the constant of integration of the given differential equation xdi+6ydy=0…

A:

Q: I'm 4-√3x + 1 2=75 2²²-7x+10

A: We can solve this as follows:

Q: By using the iterative formula Xn+1 and xo = O O 0.3652 O 1.3652 O2.6352 = 1.5, then the value of x5…

A: Find the value

Q: Deposits of $850 per month are made into an investment account. The interest rate is 6.5% per annum…

A:

Q: C. Find the DE of a family of circles with center at (1, -2). Hint: Equation of circle with center…

A:

Q: f(x, y) = JK(x² + y²) 0 20≤x≤ 30, 20 ≤ y ≤ 30 otherwise What is the value of K? (Enter your answer…

A: