Find the solution of the differential equation dy dx + x³y = 2x³ (x > 0) with the initial condition y(1) = e¯ + 2. Express your answer in explicit form. The solution is: y

Q: Solve the initial value problem y" - 5y' - 36y = 0, y(0) = a, y'(0) = -32. Find a so that the…

A: To solve the initial value problem :- y" - 5y' - 36y=0 , y(0)=α , y'(0)=-32 .

Q: Solve the laplace transforms for: a- L[alt ex. cos2x. dx]=F(s)/s b- L[t². Sin2t] =(-1)².…

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Q: Thank you understood theoretically, but unable to visualize. Can you please draw a rough diagram to…

A: As per the question we have to give a diagram helping the proof and to visulaize the phenomenon of…

Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…

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Q: 40. The cubic x³ - 2x² - x + 1 has three real roots; one is negative. a. Find a rearrangement that…

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Q: -Find the intercepts, the symmetry for the polar equation r = cos20 anc draw it.

A: A polar coordinate is represented as r, θ, where the length such that r=x2+y2 and θ is the angle…

Q: 2. the approximated roots for equationf(x) = e* - 3x in intervals [1,3] is found to be 1.34 find the…

A: Given function is fx=ex−3x. And the approximate roots for equation fx=ex−3x in intervals 1,3 is…

Q: • Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

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Q: Question 9 Use the method of reduction of order to find a second solution of the differential…

A: Introduction: When there is higher order ordinary differential equation with variable coefficients…

Q: x +y + 2z=1 2x-y-z = 0 x +2y-z = 4

A: Follow the steps below.

Q: hat is the area of the region bounded by the line x = 4 and the curve x³ = x² + 2xy - y² = 0. ht:…

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Q: Describe the level curves of the function. z = x² + 5y², c = 0, 1, 2, 3, 4 The level curves are…

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Q: (b) (c) -2a 2a T - a + 2b + 3c = 2b + b 2r + 4s 3r + 6s +2t 3t 5t С = с 11 = = 0 1 0 1 1 -3 ANS:…

A: For question number 1: Deteminant of a 2x2 matrix:Let A=abcd, then det(A)=|A|=ad-bcSimilarly for 3x3…

Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k (PUBIEN

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Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤ y ≤16, 0≤z≤ with √√y…

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Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…

A: Part (1) The set of all sets is not possible to be a set. Let us say that S is a set of all sets.…

Q: Question Create and solve a system of equations to solve the problem. A billboard painter is using a…

A: Introduction: The point where two curves meet each other is the point of their intersections. The…

Q: Q29. If we need a lot of adding and removing edges to a graph, it is better to represent the graph…

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Q: prove that u=y3-3x²y is a harmonic function determine its harmonic conjugate and find the…

A: consider u(x,y)=y3-3x2y

Q: Calculate FdV where F = 2i+2z j+yk and V is a space bounded by z=0, z = 4 and x² + y² = 9.

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Q: Use graphical methods to solve the linear programming problem. Minimize z = 4x + 5y subject to 2x -…

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Q: Find the equation of the circle passing through the points (1,5), (-2, 4), and (10,-2).

A: Using the standard equation: (x - h)2 + (y - k)2 = r2 Since it passes through the given three…

Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…

A: Please find the solution in next step

Q: Date Price 2013 $3.50s 2014 $3.58 Le 2015 $2.429 2016 $2.143 Price index

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Q: the following system of linear equations using Gaussian elimination approach (backwa tion). 1 3 3 -1…

A: Since  you have posted a multi subparts question according to guildlines I will solve first(1,2,3)…

Q: Verify that there is no magic square of order 2.

A: We will verify that there is no magic square of order 2 using the proof by contradiction.

Q: f f is a differentiable function with derivaitve f' x^2+2x-3, then f has a realtive minimum

A: We are given the derivative of the function f which is f'(x)=x2+2x-3, and we need to find relative…

Q: (B): Find the unit vector perpendicular to the vectors: 31-4/+5k ; 11+5/-6k dw (C): If w = tan x and…

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Q: The ideal gas law crates that the preccure [p], temperature [T], & volume [v] of a confined gas are…

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Q: 3. Consider the optimization problem z* = min f(x) = x₁ + x² + x² x1 + x₂ 21 Formulate the Lagrange…

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Q: Which of the following vertices are adjacent. 7

A: If two vertices are connected by an edge, they are adjacent Check the given vertices 3 and 2 are…

Q: Find AB and AC. (B): Find the unit vector perpendicular to the vectors: 3i - 4j+ 5k 4i + 5j-6k ; dw…

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Q: Solve the differential equation  4yp2-2px-y=0

A: Given: The differential equation, 4yp2-2px-y=0   To solve: The given differential equation.

Q: ..Σn n=1 n²e-n³ determine if each of the following series is convergent or divergent: 2. ∞ n=1 n+ 1…

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Q: Determine the third order polynomial below which has the following cartesian coordinades (-1,-16),…

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Q: Use the method of reduction of order to find a second differential equation t²y" — 4ty' + 6y = 0, t…

A: given second order differential equation t2y''-4ty'+6y=0, t>0 given one solution y1(t)=t2 we have…

Q: A population grows according to the logistic model 35 N = 1 +0.2e-1.3t where t is measured in years…

A: Given that a population grows according to the logistic model                        N=351+0.2e-1.3t…

Q: What are the features of the function f(x) = 2-1 graphed below? -12-11-10-9-8-7-6 as 12 11 S 10 5996…

A: The distance between the graph of a function and its asymptotes becomes 0 at the infinity. For a…

Q: The resale value V, in dollars, of a certain car is a function of the number of years t since the…

A: Given information The resale value of  car=  V ( in dollars)  Number of years = t  Base year is 2012…

Q: Question 1 a) Find the value(s) of y such that the vectors U₁ = and u₂ = are parallel. - b) Find…

A: a) Find the values of y such that the vectors u1=-6, -5, 5 and u2=-18, y, 15 are parallel. Two…

Q: Find a differential equation whose general solution is 8t y = c₁e³t+c₂e-2t

A: We have to find the differential equation whose general solution is given as ;             y = c1e8t…

Q: Q5: Find for the following functions: dx (1) In (x - y) = xy + y²; (4) y = x sinh 2x-cosh 2x (2) y =…

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Q: st rate. Consumers react to this rise ding today and spending tomorrow er, and he decides to…

A: The optimal choice for the Lili is shown below as,

Q: PS1(2) If A, B = Mn(F) and a, BE F, prove that tr (aA + BB) = a tr A + 3 tr B.

A: Prove that if A, B∈MnF and α, β∈F, then trαA+βB=α trA+β trB.

Q: Use the divergence of the vector field to compute F(x, y) = (tan-¹ (2x) fo tan¯¹ (2x) 4 where is the…

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Q: 3 where do the curve of y = cosx and y = x³ -1 intersect?

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Q: What is the distance between two points (3,-1) and (-2,-5).

A: Here given that the two points are  (3,-1) and (-2,-5) the distance between two points (x1,y1) and…

Q: Let z = exsec y Find d²z dxdy and d²z dydx

A: .

Q: The system cannot be solved by matrix inverse methods. Find a method that could be used and then…

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Q: Consider the functions f(x) g(x) 5-e7 = 35-2+6 There is an interval where the graph of g(x) lies…

A: The given functions are: fx=5e7x and gx=35x+6 It is given that there is an interval where the graph…