Question

matlab中怎么求解微分方程的精确解

Answer 1

对于相对简单的微分方程或微分方程组，可以dsolve（）函数得到解析值（精确解）。

例①：

>>syms x(t) a

>>dsolve(diff(x) == -a*x)

ans = 

C2*exp(-a*t)

>>dsolve(diff(x) == -a*x, x(0) == 1)

ans = 

exp(-a*t)

例②：

syms y(t) a

>> Dy = diff(y); D2y = diff(y,2);

>> y=dsolve(D2y == -a^2*y, y(0) == 1, Dy(pi/a) == 0)

 y = 

exp(-a*t*i)/2 + exp(a*t*i)/2

例③：

>> syms w(t)

>> Dw = diff(w); D2w = diff(w,2);

>> w = dsolve(diff(D2w) == -w, w(0)==1, Dw(0)==0, D2w(0)==0)

 w = 

exp(-t)/3 + (2*exp(t/2)*cos((3^(1/2)*t)/2))/3

Answer 2

何其难哉，利用符号工具箱看看