Ackbach said:Wolfram Development Platform (essentially Mathematica) gives a horrendous answer: extremely complicated with Hermite $H_n(x)$ functions and the hypergeometric $_1F_1$ function. In what context did this problem come up, and what have you tried?
A first order linear differential equation is a type of differential equation where the highest derivative of the dependent variable is raised to the first power and the equation can be written in the form y' + P(x)y = Q(x), where P(x) and Q(x) are functions of x.
A first order linear differential equation can be difficult because it involves finding an unknown function that satisfies the equation and can require advanced mathematical techniques to solve.
The general solution to a first order linear differential equation is a function that includes all possible solutions to the equation. It is typically expressed as y = Ce^(-∫P(x)dx) + ∫Q(x)e^(∫P(x)dx)dx, where C is a constant of integration.
The method of integrating factors involves multiplying both sides of the differential equation by an integrating factor, typically a function of x, in order to make the equation easier to solve. This method is particularly useful for first order linear differential equations with non-constant coefficients.
First order linear differential equations have many real-world applications, such as modeling population growth, predicting the spread of diseases, and analyzing the flow of fluids. They are also used in engineering and physics to understand systems that involve changing rates over time.