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]=