Please solve all problems

Problem: 1. Solve the cubic equation 2x – 7x2 – 42x + 72 = 0. Use the method of bisection to find a solution to x3 - 5 =0 correct to 4 2. significant figures. 3. Use the Newton-Raphson method to find a positive solution of the following equation, correct to 6 decimal places: cos 3x = x2 Show that the equation x3 + 3x2 – 4x – 6 = 0 has a root between x = 1 and x = 2, and use the Newton-Raphson iterative method to evaluate this root to 4 significant figures. %3D %3D 5. Find the real root of the equations: (a) x³ + 4x +3 0 (b) 5x + 2x - 1 0. 6. Solve the following equations: (b) x + 2x - 3 = 0 (a) x - 5x + 1=0 (c) x – 4x +1 = 0. 4.

Find a linear second-order differential equation F(x, y, y', y") = 0 for which y = c₁x + c₂x² is a two- parameter family of solutions. Make sure that your equa- tion is free of the arbitrary parameters c₁ and c₂. Qualitative information about a solution y = (x) of a differential equation can often be obtained from the equation itself. Before working Problems 55–58, recall the geometric significance of the derivatives dy/dx and d²y/dx².