t = var('t')
y = function('y')(t)

deq1 = diff(y, t) + y == 0
show(deq1)
desolve(deq1, [y, t])
print(desolve(deq1, [y, t])
show(desolve(deq1, [y, t])

deq2 = diff(y, t) - y == 0
show(deq2)
show(desolve(deq2, [y, t]))

deq3 = diff(y, t) + y == 1
show(deq3)
s3 = desolve(deq3, [y, t])
print(s3)
show(s3)

print(expand(s3))
show(expand(s3))

deq4 = diff(y, t) + y == cos(2 * t)
show(deq4)
desolve(deq4, [y, t])

expand(_)

sol = _

show(sol)

deq5 = diff(y, t, 2) + 4 * y == 0
show(deq5)
show(desolve(deq5, [y, t]))

deq6 = diff(y, t, 2) - 4 * y == 0
show(deq6)
show(desolve(deq6, [y, t]))

deq7 = diff(y, t, 2) + 4 * y == cos(2 * t)
show(deq7)
show(desolve(deq7, [y, t]))

deq8 = diff(y, t, 2) + 4 * y == cos(t)
show(deq8)
show(desolve(deq8, [y, t]))

deq9 = diff(y, t, 2) + 2 * diff(y, t) + 4 * y == cos(t)
show(deq9)
show(desolve(deq9, [y, t]))

deq10 = diff(y, t, 2) + 4 * diff(y, t) + 4 * y == cos(t)
show(deq10)
show(desolve(deq10, [y, t]))

deq11 = diff(y, t, 2) + 4 * diff(y, t) + 4 * y == cos(t)
show(deq11)
show(desolve(deq11, [y, t]))

deq10 = diff(y, t, 2) + 5 * diff(y, t) + 4 * y == cos(t)
show(desolve(deq10, [y, t]))

