Questions from General Calculus

Q: Plot the vector field and guess where div F > 0 and

Plot the vector field and guess where div F > 0 and where div F

Q: Solve the differential equation using the method of variation of parameters.

Solve the differential equation using the method of variation of parameters. y'' + y = sec2x, 0 < x < π/2

Q: Solve the differential equation using the method of variation of parameters.

Solve the differential equation using the method of variation of parameters. y'' + y = sec3x, 0 < x < π/2

Q: Solve the differential equation using the method of variation of parameters.

Solve the differential equation using the method of variation of parameters. y'' - 3y' + 2y = 1/1 + e-x

Q: Verify that the Divergence Theorem is true for the vector field F

Verify that the Divergence Theorem is true for the vector field F (x, y, z) = x i + y j + z k, where E is the unit ball x2 + y2 + z2 < 1.

Q: Solve the differential equation using the method of variation of parameters.

Solve the differential equation using the method of variation of parameters. y'' + 3y' + 2y = sin (ex)

Q: Solve the differential equation using the method of variation of parameters.

Solve the differential equation using the method of variation of parameters. y'' – y' + y = ex/1 + x2

Q: Solve the differential equation using the method of variation of parameters.

Solve the differential equation using the method of variation of parameters. y'' + 4y' + 4y = e-2x/x3

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

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

Q: Prove each identity, assuming that S and E satisfy the conditions

Prove each identity, assuming that S and E satisfy the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second-order partial derivative...