Find the general solution of the following differential equations.

1. 2 - 3 = 0 2. + 8 + 25 = 0 3. + 6 + 9 = 0

Determine whether the functions ₁() and ₂() are linearly independent or dependent on an

interval .

1. ₁() = cos sin and ₂() = sin 2, = (0, 1)

2. ₁() = ^2xand ₂() = ^2x, (-, )

Solve the initial value problem - 4 + 4 = 0, (1) = 1, (1) = 1

Find a particular solution to the differential equation 2 - + 5 = 6^25t. (Hint: Find first the

roots of the characteristic equation of the associated homogeneous case.)