Exam 17: Second-Order Differential Equations

The solution of the initial-value problem is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.

Use power series to solve the differential equation.

Solve the differential equation.

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

Solve the initial-value problem.

Solve the initial-value problem.

Use power series to solve the differential equation..

A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of m/s, find the position x(t) of the mass after t seconds.

Solve the differential equation.

Solve the differential equation using the method of undetermined coefficients.

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

Solve the differential equation.

A series circuit consists of a resistor an inductor with L = H, a capacitor with C = F, and a -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t.

A spring with a mass of 2 kg has damping constant 14, and a force of N is required to keep the spring stretched m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t.

Solve the differential equation.

Solve the initial-value problem.

Solve the initial-value problem.

Graph the particular solution and several other solutions.

Solve the initial-value problem using the method of undetermined coefficients.

Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.