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#!/usr/bin/env python
"""Differential equations example
Demonstrates solving 1st and 2nd degree linear ordinary differential
equations.
"""
from sympy import dsolve, Eq, Function, sin, Symbol
def main():
x = Symbol("x")
f = Function("f")
eq = Eq(f(x).diff(x), f(x))
print("Solution for ", eq, " : ", dsolve(eq, f(x)))
eq = Eq(f(x).diff(x, 2), -f(x))
print("Solution for ", eq, " : ", dsolve(eq, f(x)))
eq = Eq(x**2*f(x).diff(x), -3*x*f(x) + sin(x)/x)
print("Solution for ", eq, " : ", dsolve(eq, f(x)))
if __name__ == "__main__":
main()
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