Your factorization is incorrect. (m - 1)(m - 5) = m2 - 6m + 5, not m2 - 5m + 6.JosephK said:Homework Statement
1. Find the general solution to the differential equation:
y''-5y'+6y = 0
Homework Equations
The Attempt at a Solution
m^2 - 5m + 6 = 0
(m-1)(m-5) = 0
JosephK said:y' = Ae^x+Be^5x
(m - 3)(m - 2) ?JosephK said:This cannot be factored.
A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves the use of derivatives to model the behavior of a system and predict future values of the function.
The purpose of solving differential equations is to understand and predict the behavior of a system over time. It is a powerful tool used in many fields such as physics, engineering, economics, and biology to model and solve real-world problems.
A regular equation involves variables and constants, while a differential equation involves derivatives of a function. This means that the solution to a differential equation is a function, rather than a single value.
Some common methods for solving differential equations include separation of variables, substitution, and using special functions such as exponential and trigonometric functions. Numerical methods, such as Euler's method and Runge-Kutta methods, are also commonly used for solving differential equations.
Differential equations are used in many real-world applications, such as predicting population growth, modeling the spread of diseases, analyzing the behavior of electrical circuits, and predicting the motion of objects in physics. They are also used in finance and economics to model stock market trends and interest rates.