The equation y ′′ + y ′ − 2y = x 2 is called a differential equation because it involves an unknown function y and its derivatives y ′ and y ′′. find constants a, b, and c such that the function y = ax2 + bx + c satisfies this equation. (differential equations will be studied in detail in calculus 2).

Step-by-step explanation:

First we derive y two times

Second we replace in the differential equation y' and y'':

grouping terms

The terms on the left side must be equal to the terms of the right side, so

From 1.

From 2.

From 3.

x + 4/7

step-by-step explanation:

use cymath

combine all like terms then its just a 2 step equation