Matlab解常微分方程

dsolve('equation')

dsolve('equation','condition')

dsolve('equation','v')  给出微分方程的解析解，表示为v的函数

dsolve('equation','condition','v')

例子：

计算微分方程dy/dx+3xy=xexp(-x*x)的通解：

计算微分方程x*dy+2y-exp(x)=0在初始条件y(1)=2e的特解：

>> dsolve('Dy+3*x*y=x*exp(-x^2)','x')
 
ans =
 
C2*exp(-(3*x^2)/2) + exp(x^2/2)*exp(-(3*x^2)/2)
 
>> dsolve('x*Dy+2*y-exp(x)=0','y(1)=2*exp(1)','x')
 
ans =
 
(2*exp(1))/x^2 + (exp(x)*(x - 1))/x^2
 
>> dsolve('D2y+2*Dy+exp(x)=0','x')
 
ans =
 
C6 - exp(x)/3 + C7*exp(-2*x)