{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# Linear Differential Equations\n", "```{index} Linear Differential Equation\n", "```"]}, {"cell_type": "markdown", "metadata": {"tags": ["module-mm2"]}, "source": ["(ode_linear)=\n", "## Linear ODEs \n", "[Mathematics Methods 2](module-mm2) \n", "\n", "```{margin} Linear Operator\n", "\n", "An operator $L$ is linear if:\n", "\n", "$$ L(f + g) = Lf + Lg $$\n", "$$ L(\\lambda f) = \\lambda Lf $$\n", "\n", "for functions $f, g$ and a scalar $\\lambda$.\n", "\n", "```\n", "\n", "