In Exercises 7-10, locate the bifurcation values of a for the one-parameter family and describe the bifurcation that takes place at each such value. dy 7. dt = y+ +ay? = y6 – 2y + a 8. %3D dt dy 9. dy 10. sin y +a %3D

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A: Let uxx+uyy=0   ……………………………(1)u(0,y)=u(x,b)=0 ,  u(a,y)=u(x,0)=1 Let the solution of equation(1) by…

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: In Exercises 1–6, use Taylor’s formula for ƒ(x, y) at the origin to find quadratic and cubic…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 2 + x² + y°, the cylinder z² + y² = 2, and…

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Q: Compute for the nonhomogeneous linear DE. d²s ds + dt2 s = 0, dt ds = 0, t = 0 a. 4t + 2cost %3D dt…

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Q: Find the general solution of dy -my – ny³ dt by making a suitable substitution that transforms the…

A: Differential equation

Q: 1. a) Use the cylindrical coordinates to evaluate (3 + xy)dV, where E is the solid E in the first…

A: Here is the solution of the given problem.

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Q: 10. Let D be the solid inside the cylinder r= cos , above the xy-plane and under the paraboloid…

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Q: Answer: y = -(e-x + c)/(1 + x2)

A: Given differential equation is,

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Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 2x + 3e…

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A: We need to find dA.

Q: (2) Solve the Laplace equation with the following boundary condi- tions. Uzr + Uyy = 0, 0 < « < a,0…

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Q: 3.b) Eliminate the Ar bitrary Constants in the equation B.a) Eliminate the Arbitrary Conatanta in…

A: Using differential equations. To eliminate arbitrary constant 1.differentiate given equation as many…

Q: Consider the solid lih S,: X=4-y² そ=2

A: Surface: Surface, A two-dimensional collection of points (flat surface), a three-dimensional…

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Q: In Exercises 1–1 , evaluate the iterated integral. 1. 2xy dy dx 2. (х — у) dy dx x² + y²' *+y + 1)de…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. Let i = y?x + xŷ + z²ż, and let S be the paraboloid z = x2 + y? with 0 < z < 1. Show that fci. de…

A: Given  v→=y2x^+xy^+z2z^ and S be the paraboloid defined by  z=x2+y2      , 0≤z≤1 The boundary C of…

Q: 6. Solve the second order linear IVP d²y Y at? dy 2 = 1. "6)-1 dt (dt Hint: dt- dy substitute dy…

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Q: In Exercises 1–2, use Taylor’s formula for ƒ(x, y) at the origin to find quadratic and cubic…

A: Given: The function f(x, y)=ln(2x+y+1).

Q: Evaluate e dV where E is enclosed by the paraboloid z = 4+x² + y°, the cylinder x² + y? = 3, and the…

A: Here we have to evaluate ∫∫∫E ez dV , where E is the enclosed by the paraboloid z=4+x2+y2 , the…

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Q: In Exercises 31-42. find dy/dx. 31. y = x4 33. y = Vx 35. у %3D (2х + 5)-12-( 32. y =x-3/5 34. у Vx…

A: 31 . y=x9/4

Q: Example 6: Evaluate ez dz dy dx E Where E is enclosed by the paraboloid Z = 3+ x? + y² , the…

A: The given problem is to evaluate the given triple integral of given function ez for which region E…

Q: Evaluate e dV where E is enclosed by the paraboloid z = 4 + x² + y², the %3D cylinder x? + y² = 3,…

A: We need to evaluate integral.

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Q: .The primal form of SVR with soft margin is M 1 min |w+CE(6i + &;) i=1 s.t. y) – w"x1) – b < e+ §i,…

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Q: • Consider the 2nd order homogeneous linear diff eq: * + 2 – 3y = 0 a) Which functions below satisfy…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If (х, у) %3D х" у"is an integratingfactor of the the DE. (1+ 3ху)dx + (ху-1 +x?)dy %3 0 Then, the…

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Q: 4. Choose the one-parameter family that corresponds to each bifurcation diagram below. Briefly state…

A: [I]  dydt=Ay-y2 Equilibrium point Ay-y2=0  ⇒y=0, y=A fy=Ay-y2f'y=A-2yf'0=A,…

Q: In Exercises 1-8, use the given substitution and the Chain Rule to find dy/dx. 1. y = sin (3x + 1),…

A: since we answer only first three sub-parts so we will answer first three. Please resubmit the…