Solve the equation y' = x² - y².

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A: Given y=4-83u1=-3-41u2=-42-4

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A: Given:The equation of lemniscate is: r2=4sin2u. To find: The area inside one loop.

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Q: 3. 3 2 P + 40 -7P+2 }}

A: Given differential equation  D3+4D2-7D+2=0

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A: According to the guideline only one question can be answered. The given differential equation is…

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Q: Find Lad xdy + ydx, where C is the arc of the curve y = e for 0 ≤ x ≤ 2.

A: ∫Cxdy+ydx C: y=ex, 0≤x≤2

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Q: 4. A series RLC circuit has a hypothetical current that is described by the expression,…

A: Given i(t)=4e-2tsin(4t)  -----(1) if R  2L>1LC then i(t)= ek1t[c1cos(k2t)+c2sin(-k2t)] -----(2)…

Q: : Find the flux of the vector field F = xi + exj + zk through the surface S given by that portion of…

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Q: Determine the dependent variable independent variable type pde/ode

A: Note: “Since you have posted a question with multiple sub parts, we will provide the solution only…

Q: Find the orthogonal trajectories of the family of 2 curves x² + y² = cy A B Ⓒ с D none of the…

A: Given curve x2+y2=cy

Q: -*₁+3x₂ = 2 2x1 + x2 + 4x3 = 3 x₂ + 2x3 = 4 (a) Using [IA]~ [A¹1], Find A-¹. (b) Find Adj A.…

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: J₁/₂ ( x ) = 2 TX .sin x

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Q: 1. For each of the following sets, select all that are convex: (a) S = {(1, ₂) € R² | x² + x² ≤ 4,…

A: We shall solve first three subparts only as per the guidelines. For others kindly post again by…

Q: 6) -2x compute Joxe ²x dx Determine whether the improper divergent. Convergent (using the…

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Q: Q-1: a) Describe the domain of the function f(x) = √15x² + x − 2. b) Solve for x the equation log3…

A: (a)  We have to find the domain of f(x)=15x2+x-2 x∈Domain then…

Q: A ball is propelled straight up with an initial velocity of 250 feet/sec in a vacuum with no air…

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Q: 3. Evaluate the line integral (3ry² + 6y) da, where C' is the path traced by first moving from the…

A: The given problem is to evaluate the given line integral of (3xy2+6y) over the given path C which is…

Q: Find the value of integral Solzz (x² + y² + z²)ds, where C is parmeterized by r(t) = (cos(3t),…

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Q: (a) (i) Find the transformation matrix for T(w) = proj;(w) where = (ii) Based on the result from…

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Q: A spring with a 2-kg mass and a damping constant 2 can be held stretched 2.5 meters beyond its…

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Q: b. Solve the system (as is) using Gauss-Jacobi with initial solution of (x, y, z) = (1,0,1). Answer:…

A: 3x+7y+13z=76x+5y+3z=2812x+3y-5z=1 Initial guess x,y,z=1,0,1 The absolute relative approximate error…

Q: (c) For which integers n ≥ 1 is the function f(x) = xn convex? You may use the fact that a function…

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Q: Complete the table Equation y" - 2y + 2y exsinx = y(5)-y(3) = e2 + 2x²-5 y (4) + + 5y" + 4y = sinx +…

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Q: Area line integral Show that the value of xy² dx + (x²y + 2x) dy depends only on the area of the…

A: We know that the area bounded by the curves is evaluated using the double integral formula which is…

Q: Find the gradient vector field (F(x, y, z)) of ƒ(x, y, z) = x²y^¹ z³ 2 F(x, y, z) = (

A: Gradient vector field,  F→(x,y,z)=∇f=i.∂f∂x+j.∂f∂y+k.∂f∂z…

Q: Consider the system 3x + 7y + 13z = 76 x + 5y + 3z = 28 12x + 3y - 5z = 1

A: The given system of equations are: 3x+7y+13z=76x+5y+3z=2812x+3y-5z=1 Initial solution: x, y, z=1, 0,…

Q: The motion of a mass-spring system with damping is governed by y''(t) +10y'(t) + ky(t) = 0; y(0)=3,…

A: Given: y''t+10y't+kyt=0 , y0=3 , y'0=0 To find: y(t)

Q: b. Solve the following problems. 1. A diver jumps off a springboard 10 m above water with an initial…

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Q: F(x, y) = (4x³,3y²) along a path from (0, 0) to (2, 6). Find S F · dř. a) using a parabolic path. b)…

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Q: Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of…

A: Intercepts: If a graph cuts the x-axis at any point then, it is called the x-intercept and if the…

Q: Q1. Consider the following vectors: -- () ---- () --C) 2 3 1 3 (a) Do the vectors i, u, w span R³?…

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Q: Assume that f(r) is continuous on R, that f(r) 20 for all a € R and that lim f(x)=0= lim f(x). 84…

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Q: Using the Simplex Method, answer the questions about the following linear program. Do not solve the…

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Q: 19. Discuss the convergence of the series x²(log 2)9 + x³ (log 3)2 + x^(log 4) +

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Q: c) Let the set A = {-1,0,1} and consider the following function: f3 A × A → A × A given by f(x, y) =…

A: A function f is said to be injective or one-one if the function value corresponds to only one point…

Q: Find the points on the curve where tangents to the curve 2-2³-4y+8=0 pass through (1, 2).

A: Equation of the curve : y2-2x3-4y+8=0 The tangent passes through 1,2

Q: Suppose F(t) has the derivative f(t) shown below, and F(0) 5. Find values for F(3) and F(9) -1 3 2 1…

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Q: Activity: Find the shortest path from B to all the other vertices using Dijkstra's algorithm. Make a…

A: Dijkstra's algorithm is an algorithm to find the shortest distance between nodes in a graph.

Q: part 1 real analysis

A: Given Data: Let us consider the given operator T, Tfx =1x∫0xft dt To show that the operator T is…

Q: olve the differential equation using Laplace transform. dy +4+4y=e-2t dt y (0) = 1 y'(0) = 2 d²y dt²

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Q: Evaluate the following line integral.

A: Given that the integral ∫Cx2-2xy+y2ds where C is the upper half of circle. Here rt=5 cost, 5 sint…

Q: The motion of a mass-spring system with damping is governed by y''(t) + by' (t) + 64y(t) = 0; y(0) =…

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Q: Evaluate: f(x + x²y)ds C: r(t) = (2t, 3t), 0≤t≤1 C

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