Exact linear, nonlinear and two special types of differential equations (MM-10.7-12)

Solve the differential equation
(e^x + 2x)d^4y/dx^4 + 4(e^x + 2)dy^3/dx^3 + 6e^x d^2y/dx^2 + 4e^x dy/dx + e^x y = 1/x^5

[sandilemasuku]

Second order linear of D.E on the left side we have acceleration of the particle and on the right hand side we have force due to gravity that mechanics
On the left hand side we have the acceleration of the reaction and on the right hand side we have the source of the material, bingo i remember now, it came to me when i put solid butter in the centre of the hot pan thats when i projected a flash blueprint thought like a hologram, abstract imagination