Why not? What doesn't match?tunabeast said:[tex] \ \frac{dy}{dx} + 2y = xe^x [/tex]
... does not seem to fit the formula layout of
A linear differential equation is a mathematical equation that involves a dependent variable, its derivatives, and independent variables. The derivatives are all taken with respect to the independent variable, and the equation is linear in the dependent variable and its derivatives.
The general form of a linear differential equation is:
The solution to a linear differential equation is a function that satisfies the equation for all values of the independent variable. It can be found by integrating the equation or using other mathematical techniques, such as separation of variables or variation of parameters.
To solve a linear differential equation problem, you first need to determine the type of equation (homogeneous or non-homogeneous) and its order. Then, you can use the appropriate method (such as integrating factors, substitution, or undetermined coefficients) to find the solution. It is also important to check the solution for correctness by plugging it back into the original equation.
Linear differential equations are used in many fields of science and engineering, such as physics, chemistry, biology, economics, and engineering. They can be used to model various phenomena, such as population growth, radioactive decay, electrical circuits, and fluid dynamics. They are also used in the development of mathematical models for predicting and analyzing real-world systems and processes.