用Mathematica8解微分方程解不了,您知道是怎么回事吗?今天用Mathematica8解方程解不了了,一直报错：In[72]:=DSolve[y'[x]==E^x*y[x],y[x],x]\:6B63\:5728\:8BA1\:7B97In[72]:=DSolve::dvnoarg:Thefunctionyappearswithno

Question

用Mathematica8解微分方程解不了,您知道是怎么回事吗?
今天用Mathematica8解方程解不了了,一直报错：
In[72]:= DSolve[y'[x] == E^x*y[x], y[x], x]
\:6B63\:5728\:8BA1\:7B97In[72]:= DSolve::dvnoarg: The function y appears with no arguments. >>
Out[72]= DSolve[E^x y == E^x y[x], y[x], x]
In[60]:= DSolve[y'[x] + 2 x*y[x] == x*Exp[-x^2/2], y[x], x]
\:6B63\:5728\:8BA1\:7B97In[60]:= DSolve::dvnoarg: The function y appears with no arguments. >>
Out[60]= DSolve[E^x y + 2 x y[x] == E^(-(x^2/2)) x, y[x], x]
In[61]:= DSolve[y'[x] + y[x] == a Sin[x], y[x], x]
\:6B63\:5728\:8BA1\:7B97In[61]:= DSolve::dvnoarg: The function y appears with no arguments. >>
Out[61]= DSolve[E^x y + y[x] == a Sin[x], y[x], x]
In[62]:= DSolve[{y'[x] + y[x] == a Sin[x], y[0] == 0}, y[x], x]
\:6B63\:5728\:8BA1\:7B97In[62]:= DSolve::dvnoarg: The function y appears with no arguments. >>
In[63]:= DSolve[{E^x y + y[x] == a Sin[x], y[0] == 0}, y[x], x]
\:6B63\:5728\:8BA1\:7B97In[63]:= DSolve::dvnoarg: The function y appears with no arguments. >>
Out[63]= DSolve[{E^x y + y[x] == a Sin[x], y[0] == 0}, y[x], x]
In[64]:= DSolve[y'[x] == x, y[x], x]
\:6B63\:5728\:8BA1\:7B97In[64]:= DSolve::dvnoarg: The function y appears with no arguments. >>
Out[64]= DSolve[E^x y == x, y[x], x]
In[69]:= DSolve[{E^x y + y[x] == a Sin[x], y[0] == 0}, y, x]
\:6B63\:5728\:8BA1\:7B97In[69]:= DSolve::dvnoarg: The function y appears with no arguments. >>
Out[69]= DSolve[{E^x y + y[x] == a Sin[x], y[0] == 0}, y, x]
仔细检查过输入了,没有问题,但是解这个又可以：
In[68]:= DSolve[{x'[s] == Cos[t[s]], y'[s] == Sin[t[s]], t'[s] == s,
x[0] == 0, y[0] == 0, t[0] == 0}, {x, y, t}, s]
Out[68]= {{t -> Function[{s}, s^2/2],
x -> Function[{s}, Sqrt[\[Pi]] FresnelC[s/Sqrt[\[Pi]]]],
y -> Function[{s}, Sqrt[\[Pi]] FresnelS[s/Sqrt[\[Pi]]]]}}

Answer 1

你的软件安装有问题,我把你的输入验证了都可以有正确结果：
In[1]:= DSolve[y'[x] + 2 x*y[x] == x*Exp[-x^2/2],y[x],x]
Out[1]= {{y[x] -> E^(-(x^2/2)) + E^-x^2 C[1]}}
In[2]:= DSolve[y'[x] + y[x] == a Sin[x],y[x],x]
Out[2]= {{y[x] -> E^-x C[1] + 1/2 a (-Cos[x] + Sin[x])}}
In[3]:= DSolve[{y'[x] + y[x] == a Sin[x],y[0] == 0},y[x],x]
Out[3]= {{y[x] -> -(1/2) a E^-x (-1 + E^x Cos[x] - E^x Sin[x])}}