This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 Further Examples: DSolve Here is the solution to a second order ordinary differential equation. It uses C[1] and C[2] as the constants of integration by default. In[1]:= Out[1]= This solves the same equation, specifying that the integration constants are K[1] and K[2]. In[2]:= Out[2]= You can add constraints and boundary conditions for differential equations. In[3]:= Out[3]= This verifies the solution. In[4]:= Out[4]= Here is the solution for a Riccati-type equation. In[5]:= Out[5]= Here is the solution for an Abel-type equation. In[6]:= Out[6]= Here is the solution for a more general Abel-type equation. K\$ variables are used as dummy integration variables. In[7]:= Out[7]= Here is an equation whose solution involves Mathieu functions. In[8]:= Out[8]= Solving this equation uses a combination of methods for rational, exponential, and special function solutions, as well as reduction of order. In[9]:= Out[9]= For this equation, DSolve returns an implicit solution. In[10]:= Out[10]= The solution of this equation involves products of Airy functions. In[11]:= Out[11]= When the initial or boundary conditions are given at singularities, DSolve uses Limit internally. In[12]:= Out[12]= This equation has missing variables. In[13]:= Out[13]= The arguments of the dependent variable in differential equations should match the independent variables literally. In[14]:= Out[14]=