i got this solution so far but it isnt working pls help.

Define symbolic variable

t = var('t')

Define the function x(t) and its derivatives

x = function('x')(t) x1 = diff(x, t) x2 = diff(x1, t)

Define the differential equation

diff_eq = x^3 - 2x^2 + 5x == 0

Define initial conditions

initial_conditions = [x(0) == 0, x1(0) == 0, x2(0) == 1]

Solve the differential equation

solutions = desolve_system([diff_eq] + initial_conditions, [x(t)], ivar=t)

Display the solution

print(solutions[0])

The question is to solve the following differential equation

$x'''(t)-2x''(t)+5x'=0$, $x(0)=0$, $x'(0)=0$, $x''(0)=1$

using Laplace transform.

i got this solution so far but it isnt working pls isn't working, please help.

The question is to solve the following differential equation

$x'''(t)-2x''(t)+5x'=0$, $x(0)=0$, $x'(0)=0$, $x''(0)=1$

using Laplace transform.

i got this solution so far but it isn't working, please help.

# Define symbolic variable
t = var('t')

# Define the function x(t) and its derivatives
x = function('x')(t)
x1 = diff(x, t)
x2 = diff(x1, t)

# Define the differential equation
diff_eq = x^3 - 2*x^2 + 5*x == 0

# Define initial conditions
initial_conditions = [x(0) == 0, x1(0) == 0, x2(0) == 1]

# Solve the differential equation
solutions = desolve_system([diff_eq] + initial_conditions, [x(t)], ivar=t)

# Display the solution
print(solutions[0])