y'+e^2x-y(use linear of order one)

Question

it is differential equation under linear of order one

Answer 1

This is an expression, not an equation (no equality sign).

y'+e^2x-y=0?

If so:

y'-y=-e^2x.

Use integration factor e^-x:

e^-xy'-e^-xy=-e^2x-x,

d(e^-xy)/dx=-e^x,

e^-xy=-∫e^xdx,

y/e^x=-e^x+C, where C is an arbitrary constant,

y=-e^2x+Ce^x.

CHECK

y'=-2e^2x+Ce^x,

y'+e^2x-y=-2e^2x+Ce^x+e^2x+e^2x-Ce^x=0 (terms with the same colour cancel out).