Solve the following second-order differential equation: y" + 4y/ + 5y = 8x sin x

Q: For the following exercises, find the volume generated when the region between the curves is rotated...

A:

Q: II. Let U = R, 1 = { x eR | x5 – 26x3 + 25x = 0 }, J = { x € R | |4x + 2| > 10 } and K = { x €R | x?...

A:

Q: Find the limit: limt t→0⟨(e^5t)−1/t,t^11/(t^12−t^11),−7/8+t⟩ ⟨  ,  ,  ⟩

A:

Q: Exact Differential Equations (2xy + 1)dx + (x² + 4y)dy = 0 (18) (6xy + 2y? – 5)dx + (3x2 + 4xy – 6)d...

A: First I have written the definition of exact differential equation and it's solution rule, just use ...

Q: For the following exercises, draw the region bounded by the curves. Then, find the volume when the r...

A: Given:       y = 1/ (x+1) , x = 0 and x = 2 

Q: (2xy + 1)dx + (x² + 4y)dy = 0 (17) (18) (6xy + 2y² – 5)dx + (3x² + 4xy – 6)dy = 0

A: 17)   Given that 2xy+1dx+x2+4ydy=0  Here  M=2xy+1,       N= x2+4y Therefore     ∂M∂y=2x,            ...

Q: Find the piact farglhofthe Curve ー7 カ+6-6 2ナタナ

A:

Q: Let r(t)=(t+1)i+((t^2)−1/(t−1))j+sin⁡(−2πt)k. Then limt→1r(t)=

A:

Q: Find the general solution of = 0 y" – 2y"' + 10y":

A: Given: y(iv)-2y'''+10y''=0To find the general solution of given differential equation:General soluti...

Q: nj 00 Write out the first five terms of the sequence with, |(1 – „4)" determine n+4 n=1' whether the...

A:

Q: Question Evaluate the following limit using L'Hospital's rule. lim (e + 2a)() 6x Provide your answer...

A:

Q: A bacterial population Y is known to have a rate of growth proportional to Y itself. If between noon...

A:

Q: Let   f(x, y) = √y - 2x.              NOTE: The y - 2x is all under the square root!

A: fx,y=y-2x Since value under the root will be ≥0 So range of f will give square root of non negative ...

Q: Question 2 In the expression /In²sinx -dx, the integrand is tanx Insinx A tanx B -Insin'x + C In sin...

A: Given:- ∫ln2sinxtanxdx To Find:- Integrand from given expression

Q: Evaluate f"(e) when e = 0 given f (e) = 2 sec 30

A: Given that: f(θ)=2sec3θ

Q: y" – 3y' + 2y = 2x² + 1

A: The Solution is given below

Q: The cost of certain piece of machinery is $ 700 and its value is depreciating with time according to...

A:

Q: Sex sin x dx

A: Solving the problem by doing the integration.

Q: Suppose that f(x) = 11x² + 4x. Find: (A) f'(x) = (B) The slope of the graph of f(x) at æ = 2 and æ =...

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-  parts for...

Q: When a cake is removed from an oven, its temperature is 375°. The cake is placed in a room with a co...

A: Topic:- Calculus

Q: Homogeneous Differential Equations (13) (4x* + x³y + y*)dx + x*dy = 0

A: We are asked to solve the homogenous differential equation   

Q: Solve in detailed solution A. Í (4x³+x) v4x²+1dx B. (x+2) Vx+3dx

A: Let I=∫(4x3+x)4x2+1dxI=∫x(4x2+1)4x2+1dxI=∫x(4x2+1)(4x2+1)1/2dx I=∫x(4x2+1)32dx Put (4x2+1)=udifferen...

Q: dy 2у _ (x+2)² 9. dx'x -4 r² – 4 +

A:

Q: 3cott csc? 3tdt 5. (4+30cot3t

A:

Q: According to Hooke's Law, the force required to hold the spring stretched x m beyond its natural len...

A:

Q: Let A be the area of the region that lies under the graph of f (x) = e-* between x = 0 and x = 2. (a...

A: The given region is: f(x)=e-x ;           0≤x≤2

Q: Compute the following limits. 4-(2+h) (a) lim (b) lim - x-2 h→0

A: Using rules of limits.

Q: Find an equation of a line that is tangent to the graph of f and parallel to the given line. Functi...

A: Slope will be same and there will be 2 equations. 

Q: Find Sta | tan (ay) dy 32.

A: We have to find integral of given function.

Q: Determine the gradient of the curve 3xy + y² = -2 at the point (1, -2)

A:

Q: Find the total mass of two turns of a spring with density p in the shape of the circular helix below...

A:

Q: e' sin 0 dy 8. de 7.3:8 Solve the differential equation y sec 0

A:

Q: Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and c=⟨−2,...

A: To find the derivative of the vector function, rt=ta×b+tcWhere, a=3, -2, -3, b=1, 3, -2, and, c=-2, ...

Q: Find the values of 'a' and 'b' that make the following piecewise function differentiable everywhere....

A: We have to find the value of a and b

Q: Solve for the derivative Arc sin + Arc cos =0 y y

A:

Q: Problem 1. Set 2x f (x) = | V16+ t+dt. (a) Show that f has an inverse. (b) Find (f-1)'(0).

A:

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. ...

A:  A sequence an is convergent if it has a unique and finite limit "a".And we say that the sequence is...

Q: 7/4 26. * sec*e tan 0 de sec*0 tan*o de

A:

Q: A. Evaluate each of the following indefinite integral: 13 1.

A:

Q: write the given expression in the form of a^2 - u2: 15 + 2t - t^2 is equal to. SUBMIT YOUR SOLUTION ...

A: Given: 15+2t-t2 To write in the form:  a2-u2 15+2t-t2 = -t2-2t-15

Q: Find an equation of the plane perpendicular to the line through (2, 2, –4) and (7, –1,3) and contain...

A:

Q: Vrite out the first five terms of the sequence with, In(n) n+1 determine whether the n=1 sequence co...

A: We will find the limit 

Q: Determine the general solution for the given higher order differential equation. dz (D² + 16)³(D² + ...

A:

Q: Evaluate f"(e) when e = 0 given f (e) = 2 sec 30

A:

Q: (0–4)de 2. (6+5)

A: Given that: ∫(θ-4)(θ+5)2dθ

Q: y" + yW – 9y" – 13y" + 8y' + 12y = 0

A:

Q: Compute the directional derivative in the direction of v at the given point. f(x. y) = xy - x, v=i-j...

A:

Q: csc xcot x sin(csc x )dx

A: ∫cscx cotx sin(cscx) dx

Q: che general solution of -V - 6y = 6x3 + 26 sin 2x

A:

Q: Variable Separable (8) dx dy e 3x+2y; Provide the explicit solution (9) secx dy = sec 2ydx

A: