Use the Laplace transform to solve the given initial-value problem. y(t) = 2y+3y" - 3y - 2y = et, y(0) = 0, y'(0) = 0, y"(0) = 1

Q: Find the general solution of (x + xy²)dx + ye²² dy = 0. O ln(y² + 1) — 4e-2²² = c - O e²+2 ln(y² +…

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

Q: Solve the system using Cramer's Rule. 2x + 5y = -25 -x+3y=-4 Find the determinant D (denominator).…

A: Please refer to the image below

Q: Mark the critical points on the following graph. 20 16- -5 -4 -3 -2 -1 12 18 4 T -8 -12 Clear All…

A: The objective of the question is determine the critical points of the given graph.

Q: Solve: x"-x+ 5 y'=t y" - 4 y-2x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A:

Q: A firm faces a marginal cost (MC) function: MC = 50 - 10Q+Q² (where Q represents units of output).…

A:

Q: Find div F if F(x, y, z) = (x² + y)i + z²j + (eY - z) k.

A: Our Aim is to find the value of div F if F(x,y,z)=x2+y i +z2 j+ey-zk -(i)Let  F(x,y,z)=x2+y i +z2…

Q: Differentiate from first principle y = 5x²³² +22² +32 +4

A:

Q: An automobile company is ready to introduce a new line of cars through a national sales campaign.…

A: Given that,

Q: A trader buy's 80 mangoes. she finds that 8 are bad and a further 22 are unripe ,show on a pie chart…

A: Given data:- Total number of mangoes = 80 Bad mangoes = 8 Unripe mangoes = 22

Q: Find the volume of the solid formed by revolving the area bounded by the curve y^2 = (x^3)(1-x) in…

A: Given problem:- Find the volume of the solid formed by revolving the area bounded by the curve y2 =…

Q: Use the formula k(t) k(t) = TEREST {|r' (t) × r"(t)|| ¡|r' (t)||³ r(t) = esti + e-tj to find (t).

A: The given curve rt=e5ti+e-tj

Q: Use the basic integration rules to find or evaluate the integral. e In(2x) 1+ ln 4 [eind X X dx

A: The given integral ∫1eln2xxdx

Q: Answer true or false. F(s) = s²/(s² + 4) is not the Laplace transform of a function that is…

A:

Q: Question Find the linear approximation L(x) of the function f(x) (Enter an exact answer.) Provide…

A:

Q: Find the domain of the vector-valued function. r(t) = n(t) 0 (-∞, +∞0) O (1, + ∞ ) O (0, +∞ ) O [1,…

A: Find the domain for all three components and then take intersection of those.

Q: Solve the DE: 2 dy 3 dx 3x² + y² xy

A:

Q: Find the Wronskian of the functions f(t) = 6et sin(t) and g(t) = et cos(t). NOTE: Your answer must…

A: It is given that the Wronskian of the functions ft=6etsint and gt=etcost.   The Wronskian is given…

Q: 1. dx (x²+4)²

A:

Q: 2. cos x cos y dy-sin x siny dx = x² cos x sin y dx

A: The given equation is: cos x cos y dy-sin x sin y dx=x2cos x sin y dx Dividing it by cos x cos y we…

Q: Let f be a function defined for t 2 0. Then the integral {f(t)} =[e-stf(t) dt is said to be the…

A: We need to find Laplace.

Q: 5. L Evaluate [F DETAILS F. dr. LARCALC11 15.2.029. F(x, y) = xi + yj C: r(t) = (5t + 8)i + tj, 0…

A:

Q: If N₂- My M equation = Q, where Q is a function of y only, then the differential M + Ny' = 0 has an…

A:

Q: Find the curvature and the radius of curvature at the stated point. ㅠ r(t) = 11 cos(t)i + 10 sin(t)j…

A:

Q: 3. Find the value of (T) for a solution (x) to the initial value problem: y" + 25y = 10 cos 5x; y(0)…

A:

Q: 1. a₁ = 2n-1 an 2. An= 5n - 3 an 3. a = n(-2)

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: prove that the function f(x) = e¯* sin(x) satisfies the е differential equation ƒ (x) + ƒ'(x) = e¯ª…

A:

Q: 8. DETAILS ZILLDIFFEQMODAP11 7.2.017. Use appropriate algebra and Theorem 7.2.1 to find the given…

A:

Q: لما D the double integral of f(x, y) over D is f(x, y)dxdy = ubmit Question

A:

Q: Which are the foci of the ellipse represented by 25x² + 16y² = 400?

A:

Q: Consider the following. W = xyz, X = S + 2t, y =s - 2t, z = st² (a) Find aw/as and aw/at by using…

A:

Q: Find div F if F(x, y, z) = (x² + y)i + z² j + (ey - z) k. O 2x - 1 O 2xy - 1 O 2xi-k O 2xy i+ k

A:

Q: Consider the function f(x) = 6 - 7x² on the interval [ — 4, 3]. Find the average or mean slope of…

A:

Q: 5. Matiu is a talented furniture maker and has decided to build a bike frame out of wood. He likes…

A: Given: the two triangle connected to each other as shown in the question.

Q: Find div F and curl F if F(x, y, z) = 6evi-3 cos y j + 4 sin² z k. div F= curl F=

A:

Q: -9-8-7-6-54-3-2-1 8 7 > Next Question 1 65 6 4 3 2 + -2 -3 -5- 5 7 -6 7 -8- 9 y be 1 2 3 4 5 6 7 8 9…

A:

Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A: Break the limits according to f(t)

Q: For any vectors u, v and w, show that uxv=uxw does not always imply v = w. Prove that u v ≤ ulv, and…

A:

Q: C: boundary of the region lying between the graphs of y = 0, y = √x, and x = 9

A:

Q: 1. Calculate the following unknown quantities. (a) P= (kx 1000), r= 1.2%, t= Find S.

A: As per the rules we can answer only first question and rest can be reposted.

Q: 1. By eliminating the parameter t from the following parametric equations, find an equa- tion in…

A: As per the instruction, we will be answering the first one. For (a), Given: Now,…

Q: Find div F and curl F if F(x, y, z) = xz¹i+ 4ya²j+6z²yk. div F= curl F=

A: Vector

Q: Answer true or false. If f is not piecewise continuous on [0, ∞o>), then L{f(t)} will not exist. O…

A:

Q: Question Given F(x) below, find F'(x). Provide your answer below: F'(x) = F(x) = ™* In (6t – 3) dt

A:

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the…

A:

Q: dN dt The rate of change of N is proportional to N. (Use k for the propor kN N(t) = Cekt Evaluate…

A: We are asked to find the value of N when t = 3

Q: Find the value of the constant k so that the differential equation (e-9 + cos x + kxy)y' = y(y + sin…

A: Using the fact that an exact differential if dM/dy=dN/dx

Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

A:

Q: Can you present the solution in a different format. I do not understand what the solution is…

A: Let's solve given diffrential integration.

Q: Solve the given initial value problem. 0x²y² + xy³ = 2 0x²y² + y² = 3 ○ xy² + xy³ = 0 Oxy²y³ = 1…

A:

Q: Please

A: