Question

Verify that the indicated function y = ϕ(x) is an explicit solution of the given first-order differential equation. (y − x)y' = y − x + 8; y = x + 4 x + 3

Answer 1

The function
`y = x + 4x - 3` is not a solution of the given differential equation.

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.

`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\\\\`

The function
`y = 5x - 3` is not a solution of the given differential equation