Disorganized series

solve、dsolve

clc,clear;
syms m V rho g k;
% Solving differential equations ( The solution is to satisfy the differential equation   The relationship between variables ）
dsolve('Dy==5')  %dy/dt=5
dsolve('Dy==x','x') %dy/dx=x  If no variable is specified, it defaults to t
dsolve('D2y==1+Dy','y(0)==1','Dy(0)==0')%d2y/dt2=1+dy/dt, Initial conditions y(0)=1,dy(0)/dt=0
[y1,y2]=dsolve('Dx==y+x','Dy==2*x','x(0)==0','y(0)==1')%dx/dt=y+x,dy/dt=2*x,x(0)=0,y(0)=1,x=y5,y=y6

% Symbolic variables are defined in advance , You can write an expression directly in function brackets , No quotes ;
% If there is no definition, put it in quotation marks 
%solve Solution of general equations 
syms x y a;
eq=x^2+2*x+1;
s1=solve(eq,x)
eq=a*x+2;
s2=solve(eq,a)
eq1=x+2*y-8; % Solve a system of binary first-order equations , Solution is a structure 
eq2=3*x+5*y-4;
s3=solve(eq1,eq2,x,y);% Only s3 Bearing result s3 For vector group , You can use [x,y] Undertaking 
s3=[s3.x,s3.y]

s1=solve(sin(x)==1/2)
s2=solve(x^3-1==0)

%ode For solving numerical solutions of differential equations , See for example CSDN, The point is 
% Standard form of differential equation , You can always find multiple variables   Such as F(y,y',y'',y''',…,t)=0
%y,y',y'',y''' It's a variable , To set a vector , Do variable substitution 
% Like a vector x：  x(1)=y,x(2)=y'
%ode45  The main part of the function   List each variable separately   Yes t Derivative  d x(2)  The expression of 

vpa,simplify,subs

syms x y z 
f=cos(x)^2-sin(x)^2
s1 = simplify(f) 
s1 = cos(2*x) 
%  Do not match the file name with matlab The inherent function name is the same ！！！
clc,clear;
syms m V rho g k;

s=dsolve('m*D2s=m*g-rho*g*V-k*Ds','s(0)=0','Ds(0)=0')
% The differential equation has only one variable s, Or say   The solution of the differential equation is s And t The relation of 

s=subs(s,{
    m,V,rho,g,k},{
    239.46,0.2058,1035.71,9.8,0.6})
%  R = subs(S, old, new)  utilize new Instead of the symbol ！ expression ！ in old Value 

s=vpa(s,10) 
% The exact solution obtained when using symbolic calculation will show scores , It can be used vpa Convert to decimal display 
%vpa The action object can be numeric or ！ expression ！（ Numerical precision in expressions ）（ Significant figures ）

%s=dsolve('m*DV==m*g-rho*g*V-K*V')

syms f(x)
a=1/99
x=sym(1/2)
y=vpa(x)