Question

Solve the given initial-value problem.

(d ^ 2 * x)/(d * t ^ 2) + 4x = - 4sin(2t) + 7cos(2t), x(0) = - 1, x' * (0) = 1
x(t) = 7/4 * t * sin(2t) + t * cos(2t) -cos(2t)|

Answer 1

The solution is x(t) = -t*cos(2t) + t*sin(2t) - cos(2t).

To solve the given initial-value problem, we can use the method of undetermined coefficients.

First, we find the complementary solution by solving the homogeneous equation (d²*x)/(d*t²) + 4x = 0.

The characteristic equation is r² + 4 = 0, which has complex roots ₁ = -2i and r₂ = 2i.

So, the complementary solution is X