如图所示,求解的是一个代数常微分方程组,前三组是odes,后面四组方程是代数边界条件(a,b,c,d都是常数),一直求不出来u[r],v[r],p[r]的解析表达式,求指点!
然后源代码如下:
Clear["Global`*"];
Print["函数解析式的求解:"];
DSolve[{u[r] + m v[r] + r Derivative[1][u][r] ==
0, -(c11 + c99 m^2 - r^2 \[Rho] \[Omega]^2) u[r] - (c11 + c99) m v[
r] + r (-r Derivative[1][p][r] + c11 Derivative[1][u][r] +
c12 m Derivative[1][v][r] + c69 m Derivative[1][v][r] +
c11 r (u^\[Prime]\[Prime])[r]) ==
0, -m r p[r] + (c11 + c99) m u[r] + c99 v[r] + c11 m^2 v[r] -
r^2 \[Rho] \[Omega]^2 v[r] + c12 m r Derivative[1][u][r] +
c69 m r Derivative[1][u][r] - c66 r Derivative[1][v][r] -
c66 r^2 (v^\[Prime]\[Prime])[r] ==
0, -a p[a] + c12 u[a] + c12 m v[a] + a c11 Derivative[1][u][a] ==
0, -b p[b] + c12 u[b] + c12 m v[b] + b c11 Derivative[1][u][b] ==
0, -c69 m u[a] - c69 v[a] + a c66 Derivative[1][v][a] ==
0, -c69 m u[b] - c69 v[b] + b c66 Derivative[1][v][b] == 0}, {u[r],
v[r], p[r]}, r]