DSolve[-x^(-5) + E^x*y[x] + 4*E^x*Derivative[1][y][x] + 6*E^x*Derivative[2][y][x] + 4*(2 + E^x)*Derivative[3][y][x] + (E^x + 2*x)*Derivative[4][y][x] == 0,y[x],x]