Differential Equations Test #2

Chapter 2 ONLY

Provided list of integrals.

(sec 2.2) Solve x’’-x’-12x = 0.

(sec 2.2) Solve x’’+4x’+4x = 0.

(sec 2.2) If the eigenvalues are λ=6 and λ=-2, then find the DE.

(sec 2.2) Solve the DE x’’+2x’+5x = 0.

(sec 2.2) Solve x’’+7x = 0, x(0)=1 and x’(0)=2.

Solve x’’+3x = 4e^-5t.

(sec 2.3) Find the general solution of x’’-x’+7x = 5t-3

(sec 2.3) Find the general solution of x’’-x = 5e^-t.

(sec 2.3) Solve IVP of x’’+2x = sin3t, x(0)=1 and x’(0)= -1.

(sec 2.3) Consider an RCL circuit with R = 2, L = C = 1, with current being driven by an electromotive force of 2 sin 2t. The circuit equation for the charge Q(t) across the capacitor is Q′′ +2Q′ +Q = 2 sin 2t, with Q(0) = 4 and Q′(0) = 0. Solve the equation.

(sec 2.5) Solve the nonhomogeneous DE of x′′′ − 2x′′ − 3x′ = 5e^4t.