Solving non linear 2nd order differential equation

I am trying to solve the differential equation:

mx''+cx'+kx=ky+cy''

y is the input and x is the output.

y=Y0sin(wt)

where m=100, c=1300, k= 17000, Y0=input value, w=input value

initially I need to solve this, and then i need to plot displacement and velocity profiles.

clear
t=0:0.1:15;                                          %time peroid
Y0= input('wave amplitude ') ;                        %Wave amplitude
l= input('length of wave ') ;                        %length of the wave
u=input('speed of boat');                            %Boat Velocity
w=u/l;                                               %frequency of wave
y=Y0*sin(w*t);                                       %wave height model

Dr=0.5;                                              %Required Damping Ratio
k=17000;                                             %Spring Constant of suspension
m=100;

wn=(k/m)^0.5;                                        %Natural Frequency
wd=wn*(1-Dr^2)^0.5;                                  %Damped Natural Frequency
                             
c=2*Dr*(k*m)^(0.5);                                 %Damping coefficient

syms x(t)
ode=m*diff(x,t,2)+c*diff(x,t)+k*x==y+(2*Dr/wn)*diff(y,t);
xSol(t)=dsolve(ode);

Answer 1

[Birdman]

Try this:

clear
syms t                                     
Y0= input('wave amplitude ') ;                        %Wave amplitude
l= input('length of wave ') ;                        %length of the wave
u=input('speed of boat');                            %Boat Velocity
w=u/l;                                               %frequency of wave
y=Y0*sin(w*t);                                       %wave height model
Dr=0.5;                                              %Required Damping Ratio
k=17000;                                             %Spring Constant of suspension
m=100;
wn=(k/m)^0.5;                                        %Natural Frequency
wd=wn*(1-Dr^2)^0.5;                                  %Damped Natural Frequency             
c=2*Dr*(k*m)^(0.5);                                 %Damping coefficient

syms x(t)
Dx(t)=diff(x,t);
ode=m*diff(x,t,2)+c*diff(x,t)+k*x==y+(2*Dr/wn)*diff(y,t);
xSol(t)=dsolve(ode,[x(0)==0 Dx(0)==0]);%displacement
DxSol(t)=diff(xSol,t);%velocity
t=0:0.05:15;
plot(t,xSol(t),t,DxSol(t))

[Reuben Salisbury]

That's great, thank you so much!