Using the D$-$operator method, get complete specific solutions, including the constants of integration

d$.3\frac{dx}{dt}+5\frac{x}{|x|}\sqrt[\phantom{2}]{|x|}-20=2sin(6\mathrm{.}28t),x(0+)=15$

e$.9760x^3-2000=-\frac{d^{2}x}{d{t}^2}-50\frac{dx}{d{t}^2}-50\frac{dx}{dt},x(0+)=0,x(0+)=0$