Questions from General Calculus

Q: Solve the boundary-value problem, if possible. y''

Solve the boundary-value problem, if possible. y'' + 16y = 0, y (0) = -3, y (π/8) = 2

Q: Find a parametric representation for the surface. The part of

Find a parametric representation for the surface. The part of the plane z = x + 3 that lies inside the cylinder x2 + y2 = 1

Q: Solve the boundary-value problem, if possible. y''

Solve the boundary-value problem, if possible. y'' + 4y' + 4y = 0, y (0) = 2, y (1) = 0

Q: Solve the boundary-value problem, if possible. y''

Solve the boundary-value problem, if possible. y'' - 8y' + 17y = 0, y (0) = 3, y (π) = 2

Q: Prove the identity, assuming that the appropriate partial derivatives exist and

Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f is a scalar field and F, G are vector fields, then f F, F ∙ G, and F Ã...

Q: Solve the boundary-value problem, if possible. 4y''

Solve the boundary-value problem, if possible. 4y'' - 4y' + y = 0, y (0) = 4, y (2) = 0

Q: Solve the boundary-value problem, if possible. y''

Solve the boundary-value problem, if possible. y'' + 4y' + 20y = 0, y (0) = 1, y (π) = 2

Q: Solve the boundary-value problem, if possible. y''

Solve the boundary-value problem, if possible. y'' + 4y' + 20y = 0, y (0) = 1, y (π) = e-2π

Q: Let L be a nonzero real number. (a).

Let L be a nonzero real number. (a). Show that the boundary-value problem y'' + λy = 0, y (0) = 0, y (L) = 0 has only the trivial solution y – 0 for the cases λ = 0 and λ < 0. (b). For the case λ > 0,...

Q: If a, b, and c are all positive constants and

If a, b, and c are all positive constants and y (x) is a solution of the differential equation ay'' + by' + cy = 0, show that lim x→∞ y (x) = 0.