dsolve solves a differential equation. Print the general solution of y' = y.

Goal

Solve y' = -k y.

import sympy as sp
x = sp.symbols('x')
y = sp.Function('y')
print(sp.dsolve(sp.diff(y(x), x) - y(x), y(x)))

import sympy as sp
t = sp.symbols('t')
y = sp.Function('y')
k = sp.symbols('k', positive=True)
print(sp.dsolve(sp.diff(y(t), t) + k * y(t), y(t)))

import sympy as sp
x = sp.symbols('x')
y = sp.Function('y')
print(sp.dsolve(sp.diff(y(x), x, 2) + y(x), y(x)))

import sympy as sp
x = sp.symbols('x')
y = sp.Function('y')
print(sp.checkodesol(sp.diff(y(x), x) - y(x), sp.dsolve(sp.diff(y(x), x) - y(x), y(x))))