The Wolfram Language's differential equation solving functions can be applied to many different classes of differential equations, automatically selecting the appropriate algorithms without needing preprocessing by the user.
Use DSolve to solve the differential equation for with independent variable :
The solution given by DSolve is a list of lists of rules. The outermost list encompasses all the solutions available, and each smaller list is a particular solution.
If not enough initial conditions are given, constants C[n] are returned:
First, solve the differential equation using DSolve and set the result to solution:
Use =, /., and Part to define a function g[x] using solution:
Define a table of functions t[x] for integer values of C between 1 and 10:
Use Plot to plot the table over the range :