In[1]=DSolve[{y'[x] + y[x] == a Sin[x], y[0] == 0}, y[x], x]
Out[1]={{y[x] -> -(1/2)
a \[ExponentialE]^-x (-1 + \[ExponentialE]^
x Cos[x] - \[ExponentialE]^x Sin[x])}}
In[1]=linearequation = y'[t] - 3*t*y[t] == 1;
In[2]=generalsolution = DSolve[linearequation, y[t], t]
Out[2]={{y[t] -> \[ExponentialE]^((3 t^2)/2) C[1] + \[ExponentialE]^((3 t^2)/
2) Sqrt[\[Pi]/6] Erf[Sqrt[3/2] t]}}
In[3]=particularsolution = DSolve[{linearequation, y[0] == 4}, y, t]
Out[3]={{y -> Function[{t},
1/6 \[ExponentialE]^((3 t^2)/
2) (24 + Sqrt[6 \[Pi]] Erf[Sqrt[3/2] t])]}}
以上举了2个例子(直接复制,一些符号有变化).
其实在帮助文件里面都有详细介绍,可以查询
http://www.chinavib.com/forum/archiver/tid-4874.html
在这里看一看