Let {{MATH_1}} be a function with {{MATH_2}}, and {{MATH_3}} is a solution to the differential equation (DE) {{MATH_4}} Use the linear approximation of {{MATH_5}} near {{MATH_6}} to approximate {{MATH_7}}. {{CMD_8}} We will approximate {{MATH_9}} with {{MATH_10}}, where {{MATH_11}} is the linear approximation of {{MATH_12}} at {{MATH_13}}. {{CMD_14}} {{CMD_15}} In order to find {{MATH_16}}, the linear approximation of {{MATH_17}} at {{MATH_18}}, we need to find both {{MATH_19}} and {{MATH_20}}. {{CMD_21}} {{CMD_22}} In order to find {{MATH_23}}, the linear approximation of {{MATH_24}} at {{MATH_25}}, we need to find both {{MATH_26}} and {{MATH_27}}. We already know that {{MATH_28}}. Now we have to find {{MATH_29}}. {{CMD_30}} {{CMD_31}} In order to find {{MATH_32}}, the linear approximation of {{MATH_33}} at {{MATH_34}}, we need to find both {{MATH_35}} and {{MATH_36}}. We already know that {{MATH_37}}. Now we have to find {{MATH_38}}.