Use incorrect question as sample for format of answer of question you are answering **Find a general solution for the given differential equation with x as the independent variable.**\[ y''' + 7y'' - 26y' - 72y = 0 \]---A general solution with x as the independent variable is \( y(x) = \) ________. ### Differential Equations**Problem 6.2.4****Objective:** Find a general solution for the given differential equation with \( x \) as the independent variable.**Given Differential Equation:**\[ y''' - 2y'' - 40y' - 64y = 0 \]**Solution:**A general solution with \( x \) as the independent variable is given by:\[ y(x) = C_1 e^{-2x} + C_2 e^{8x} + C_3 e^{-4x} \]Where:- \( y(x) \) is the function we seek as a solution.- \( C_1, C_2, \) and \( C_3 \) are constants determined by boundary or initial conditions.**Explanation:**The given differential equation is a third-order linear homogeneous differential equation. The solution is formed by finding the characteristic equation and solving for the roots, which can then be used to form the general solution as a combination of exponential functions.### Notes:- This problem involves solving higher-order differential equations, which are frequently encountered in various fields such as physics and engineering.- Understanding and finding characteristic equations is crucial for solving such differential equations.

Name: Use incorrect question as sample for format of answer of question you
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: Use incorrect question as sample for format of answer of question you are answering **Find a general solution for the given differential equation with x as the independent variable.**\[ y''' + 7y'' - 26y' - 72y = 0 \]---A general solution with x as t