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毫无章法系列
2022-07-05 17:16:00 【Selvaggia】
solve、dsolve
clc,clear;
syms m V rho g k;
%微分方程求解(解就是满足微分方程的 变量之间的关系式)
dsolve('Dy==5') %dy/dt=5
dsolve('Dy==x','x') %dy/dx=x 没指定变量则默认为t
dsolve('D2y==1+Dy','y(0)==1','Dy(0)==0')%d2y/dt2=1+dy/dt,初始条件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
%提前定义了符号变量,就可以直接在函数括号里写表达式,不用加引号;
%没定义那么就放在引号里
%solve对一般方程的求解
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; %解二元一次方程组,解是个结构体
eq2=3*x+5*y-4;
s3=solve(eq1,eq2,x,y);%只用s3承载结果则s3为向量组,可用[x,y]承接
s3=[s3.x,s3.y]
s1=solve(sin(x)==1/2)
s2=solve(x^3-1==0)
%ode用于求微分方程的数值解,实例见CSDN,重点在于
%微分方程的标准形式,总能找出多个变量 如F(y,y',y'',y''',…,t)=0
%y,y',y'',y'''就是变量,要设一个向量,做变量替换
%如向量x: x(1)=y,x(2)=y'
%ode45 函数主要部分 要分别列出每个变量 对t求导的 d x(2) 的表达式
vpa,simplify,subs
syms x y z
f=cos(x)^2-sin(x)^2
s1 = simplify(f)
s1 = cos(2*x)
% 文件名不要与matlab固有函数名重名!!!
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')
%该微分方程只有一个变量s,或者说 微分方程的解就是s与t的关系式
s=subs(s,{
m,V,rho,g,k},{
239.46,0.2058,1035.71,9.8,0.6})
% R = subs(S, old, new) 利用new的值代替符号!表达式!中old的值
s=vpa(s,10)
%使用符号计算时得到的精确解会出现分数,可以用vpa转换为小数显示
%vpa作用对象可以是数值或者!表达式!(表达式中的数值精度)(有效数字)
%s=dsolve('m*DV==m*g-rho*g*V-K*V')
syms f(x)
a=1/99
x=sym(1/2)
y=vpa(x)
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