Answer:
The function [tex]y = x + 4x - 3[/tex] is not a solution of the given differential equation.
Step-by-step explanation:
Verify that a function f (x) is a solution to a differential equation, consists in finding the derivatives of the function and entering them into the equation. If the given function, indeed, is the solution, equality must be checked.
[tex]y = x + 4x +3 = 5x+3\\\\y' = 5\\\\\left(y - x\right)y' = y - x + 8\\\\\left(5x + 3 - x\right)\left(5\right) = 5x + 3 - x + 8\\\\\left(4x + 3\right)\left(5\right) = 4x + 11\\\\20x + 15 = 4x + 11\\\\[/tex]
The function [tex]y = 5x - 3[/tex] is not a solution of the given differential equation
