clc; clear; close all; %%represent u by using syms to create function u(t) syms u(t) %%assume that L_0=20; v_0=0.0001; v

[answerhappygod]

clc;
clear;
close all;
%%represent u by using syms to create function u(t)
syms u(t)
%%assume that
L_0=20;
v_0=0.0001;
v_1=0.0001;
A=pi*0.007^2;
rho=1000;
g=9.81;
C_d=0.001; %%damping cost, stabilizes numbers
lambda=L_0-2*v_0*t;
%%define theta
theta=3*(2*pi*A*rho*u_3(t)*lambda(t)*(g*cosu_1(t)+2*v_1*u_2(t)sinu_1(t))+4*pi*C_d*u_2(t))+3*diff(lamdba(t),1)*(pi*A*rho*u_3(t)^2*u_2(t)+A*rho*(A+pi*lamba(t)^2)u_2(t));
N=A*rho*lambda*(3*A+3*pi*u_3(t)^2+pi*lambda(t)^2);
%%first order system
ode1 = diff(u_1) == u_2;
ode2 = diff(u_2) == -theta/N;
ode3 = diff(u_3) == 2*v_1*sin*u_1;
odes = [ode1; ode2; ode3];
%%conditions
rho1(0)=0;
rho2'(0)=0;
delta(0)=0.01;
cond = [rho1;rho2;delta];
%%solve sysrem by dsolve function. We have interval [0, 20]
sol=dsolve(eqn,cond);
fplot(sol,[0,20]);
grid on;