eq.py

Created on January 07, 2025
2.46 KB
def menu():
    print("=== Résolution d'Équations Différentielles ===")
    print("1. Équation différentielle du 1er degré")
    print("2. Équation différentielle du 2nd degré")
    print("0. Quitter")
    choix = int(input("Choisissez une option : "))
    return choix

def solve_first_order():
    print("\n--- Équation différentielle du 1er degré ---")
    print("Forme : y'(x) + P(x)y(x) = Q(x)")
    
    P = float(input("Entrez le coefficient P(x) constant : "))
    Q = float(input("Entrez le coefficient Q(x) constant : "))
    
    print("\nÉtapes :")
    print("1. Calculer le facteur intégrant μ(x) = exp(∫P(x)dx)")
    print("   Ici, μ(x) = exp(" + str(P) + "*x)")
    print("2. Multiplier toute l'équation par μ(x).")
    print("3. Résoudre la dérivée totale résultante.")
    
    print("\nSolution générale :")
    print("y(x) = (1/" + str(P) + ")*(" + str(Q) + ")*exp(-" + str(P) + "*x) + C*exp(-" + str(P) + "*x)")

def solve_second_order():
    print("\n--- Équation différentielle du 2nd degré ---")
    print("Forme : ay''(x) + by'(x) + cy(x) = 0")
    
    a = float(input("Entrez le coefficient a : "))
    b = float(input("Entrez le coefficient b : "))
    c = float(input("Entrez le coefficient c : "))
    
    print("\nÉtapes :")
    print("1. Résoudre l'équation caractéristique : ar2 + br + c = 0")
    
    delta = b**2 - 4*a*c
    print("   Discriminant ∆ = " + str(delta))
    
    if delta > 0:
        r1 = (-b + delta**0.5) / (2*a)
        r2 = (-b - delta**0.5) / (2*a)
        print("   Racines réelles distinctes : r1 = " + str(r1) + ", r2 = " + str(r2))
        print("   Solution : y(x) = C1*exp(" + str(r1) + "*x) + C2*exp(" + str(r2) + "*x)")
    elif delta == 0:
        r = -b / (2*a)
        print("   Racines réelles doubles : r = " + str(r))
        print("   Solution : y(x) = (C1 + C2*x)*exp(" + str(r) + "*x)")
    else:
        real = -b / (2*a)
        imag = (abs(delta)**0.5) / (2*a)
        print("   Racines complexes : " + str(real) + " ± " + str(imag) + "i")
        print("   Solution : y(x) = exp(" + str(real) + "*x)*(C1*cos(" + str(imag) + "*x) + C2*sin(" + str(imag) + "*x))")

def main():
    while True:
        choix = menu()
        if choix == 1:
            solve_first_order()
        elif choix == 2:
            solve_second_order()
        elif choix == 0:
            print("Au revoir !")
            break
        else:
            print("Choix invalide, veuillez réessayer.")

# Lancer le programme
main()