Differential equation solution not shown by SymPy

Question

In the following code, I first solve a differential equation, but, then, when I check to see if it is a solution, it appears not to be. (The following code returns False.) What am I doing wrong?

import sympy as sy

t = sy.symbols('t')
y = sy.symbols('y', cls=sy.Function)

expr = y(t).diff(t, t) + 3*y(t).diff(t) + 2*y(t) - 4*t
solution = sy.dsolve(sy.Eq(expr, 0)).rhs

print(expr.subs(y(t), solution).simplify() == 0)

Answer 1

You need doit() to effectively evaluate the derivative: expr.subs(y(t), solution).doit()

import sympy as sy

t = sy.symbols('t')
y = sy.symbols('y', cls=sy.Function)

expr = y(t).diff(t, t) + 3*y(t).diff(t) + 2*y(t) - 4*t
solution = sy.dsolve(sy.Eq(expr, 0)).rhs

print(expr.subs(y(t), solution).doit().simplify() == 0)

Prints True

Answer 2

If you only want to check the solution, checkodesol can be used:

>>> checkodesol(expr, solution)
(True, 0)

(It automatically handles the simplification and other details that might complicate checking a solution.)