matlab学习5-解微积分方程

1、 dsolve解微分方程

dsolve('Du=1+u^2','t')

微分方程组

y=dsolve('D2y+4*Dy+29*y=0','y(0)=0,Dy(0)=15','x')

[x,y,z]=dsolve('Dx=2*x-3*y+3*z','Dy=4*x-5*y+3*z','Dz=4*x-4*y+2*z', 't');
simplify(x)%将x化简
simplify(y)
simplify(z)

微分方程的数值解

建立m文件

function dy=fun(t,y)
    dy=zeros(2,1);
    dy(1)=y(2);
    dy(2)=1000*(1-y(1)^2)*y(2)-y(1);

命令ode15s

[T,Y]=ode15s('fun',[0 3000],[2 0]);
plot(T,Y(:,1),'-')