Exact Equations

Here is an example of an exact ODE.
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
In[4]:=
Click for copyable input
Out[4]=
In[5]:=
Click for copyable input
Out[5]=
This verifies the solution.
In[6]:=
Click for copyable input
Out[6]=
Here is a contour plot of the solution.
In[7]:=
Click for copyable input
Out[7]=

If an equation is not exact, it may be possible to find an integrating factor (a multiplier for the functions and , defined previously) that converts the equation into exact form. DSolve tries a variety of techniques to automatically find integrating factors in such situations.