syms

创建符号变量(或数组)和方程

diff

diff函数式用于求导数和差分的.
微分方程

dsolve

与solve函数类似可以使用向量式输入

一阶微分方程$dÿ/dt=ty$

syms y（t）
ode = diff（y，t）== t * y
ode（t）= diff（y（t），t）== t * y（t）
ySol（t）= dsolve（ode）

如果增加一个条件y(0) = 2

1 2	cond = y(0) == 2; ySol(t) = dsolve(ode,cond)

$(dy/dt+y)^2=1,y(0)=0.$

syms y(t)
ode = (diff(y,t)+y)^2 == 1;
cond = y(0) == 0;
ySol(t) = dsolve(ode,cond)

$du/dt=3u+4v,dv/Sdt=−4u+3v.$

syms u(t) v(t)
%Define the equations using == and represent differentiation using the diff function.

ode1 = diff(u) == 3*u + 4*v;
ode2 = diff(v) == -4*u + 3*v;
odes = [ode1; ode2]
%odes(t) =
 diff(u(t), t) == 3*u(t) + 4*v(t)
 diff(v(t), t) == 3*v(t) - 4*u(t)
%Solve the system using the dsolve function which returns the solutions as elements of a structure.

S = dsolve(odes)

参考

dsolve csdn