matlab一阶微分方程的解法

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matlab一阶微分方程的解法

Examples:
dsolve('Dx = -a*x') returns
ans = exp(-a*t)*C1
x = dsolve('Dx = -a*x','x(0) = 1','s') returns
x = exp(-a*s)
y = dsolve('(Dy)^2 + y^2 = 1','y(0) = 0') returns
y =
[ sin(t)]
[ -sin(t)]
S = dsolve('Df = f + g','Dg = -f + g','f(0) = 1','g(0) = 2')
returns a structure S with fields
S.f = exp(t)*cos(t)+2*exp(t)*sin(t)
S.g = -exp(t)*sin(t)+2*exp(t)*cos(t)
Y = dsolve('Dy = y^2*(1-y)')
Warning:Explicit solution could not be found; implicit solution returned.
Y =
t+1/y-log(y)+log(-1+y)+C1=0
dsolve('Df = f + sin(t)','f(pi/2) = 0')
dsolve('D2y = -a^2*y','y(0) = 1,Dy(pi/a) = 0')
S = dsolve('Dx = y','Dy = -x','x(0)=0','y(0)=1')
S = dsolve('Du=v,Dv=w,Dw=-u','u(0)=0,v(0)=0,w(0)=1')
w = dsolve('D3w = -w','w(0)=1,Dw(0)=0,D2w(0)=0')
y = dsolve('D2y = sin(y)'); pretty(y)

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