Linear ordinary differential equations (ODEs) are equations that involve an unknown function and its derivatives, where the unknown function and its derivatives appear linearly. This means that the equation can be expressed in the form $$a_n(t)y^{(n)} + a_{n-1}(t)y^{(n-1)} + ... + a_1(t)y' + a_0(t)y = g(t)$$, where the coefficients $$a_i(t)$$ are functions of the independent variable, and $$g(t)$$ is a known function. These equations are crucial for modeling many physical systems and can be solved using various methods, including the Laplace transform technique.
congrats on reading the definition of linear ordinary differential equations. now let's actually learn it.