DSolve[{Derivative[1][x1][t] == a*x2[t] + b*Cos[c*t]*x3[t] + b*Sin[c*t]*x4[t], Derivative[1][x2][t] == -(a*x1[t]) + b*Sin[c*t]*x3[t] - b*Cos[c*t]*x4[t], Derivative[1][x3][t] == -(b*Cos[c*t]*x1[t]) - b*Sin[c*t]*x2[t] + a*x4[t], Derivative[1][x4][t] == -(b*Sin[c*t]*x1[t]) + b*Cos[c*t]*x2[t] - a*x3[t]},{x[t], y[t], z[t]},t]