Not a member of GistPad yet?
Sign Up,
it unlocks many cool features!
- 1st question
- import numpy as np
- A = np.matrix("8 -8 -2; 4 -3 -2; 3 -4 1")
- print("A :", A)
- ev1, ev2 = np.linalg.eig(A)
- print("Eigen Values :", ev1)
- print("Eigen Vector :", ev2)
- 3rd question
- import math
- eqn = input("Enter the function in terms of x (e.g., x**3 - x - 2): ")
- a = float(input("Enter interval start (a): "))
- b = float(input("Enter interval end (b): "))
- tol = float(input("Enter tolerance (e.g., 0.0001): "))
- fa = eval(eqn, {"x": a, "math": math})
- fb = eval(eqn, {"x": b, "math": math})
- if fa * fb >= 0:
- print("Root does not lie in this interval.")
- else:
- while (b - a) / 2 > tol:
- mid = (a + b) / 2
- f_mid = eval(eqn, {"x": mid, "math": math})
- if f_mid == 0:
- break
- elif eval(eqn, {"x": a, "math": math}) * f_mid < 0:
- b = mid
- else:
- a = mid
- print(f"\nApproximate Root: {((a + b) / 2):.5f}")
- 5th question
- x, y, z, w = 0.0, 0.0, 0.0, 0.0
- n = 15
- print(f"{'k':<4} {'x':<12} {'y':<12} {'z':<12} {'w':<12}")
- for k in range(1, n+1):
- x_new = (6 + y - 2*z) / 10
- y_new = (25 + x + z - 3*w) / 11
- z_new = (-11 - 2*x + y + w) / 10
- w_new = (15 - 3*y + z) / 8
- x, y, z, w = x_new, y_new, z_new, w_new
- print(f"{k:<4} {x_new:<12.4f}{y_new:<12.4f}{z_new:<12.4f}{w_new:<12.4f}")
- 7th question
- print("Choose M(x,y):")
- print("1. M = x*y")
- print("2. M = x + y")
- m_choice = int(input("Enter your choice for M: "))
- print("\nChoose N(x,y):")
- print("1. N = x**2/2")
- print("2. N = x - y")
- n_choice = int(input("Enter your choice for N: "))
- def dM_dy(x):
- if m_choice == 1:
- return x
- elif m_choice == 2:
- return 1
- def dN_dx(x):
- if n_choice == 1:
- return x
- elif n_choice == 2:
- return 1
- x = 2
- if dM_dy(x) == dN_dx(x):
- print("\nThe differential equation is Exact")
- else:
- print("\nThe differential equation is Not Exact")
- 9th question
- from sympy import symbols, Function, dsolve, Eq
- x = symbols('x')
- y = Function('y')
- eq = Eq(y(x).diff(x, 2) - 8*y(x).diff(x) + 15*y(x), 0)
- solution = dsolve(eq)
- print("y =", solution.rhs)
RAW Paste Data
Copied
