y' + y = e^x ; y(0) = 1

1st, i calculate the integrating factor...

u(x) = e^x

times the integrating factor with DE...

y'e^x + ye^x = e^2x

dy/dx e^x + ye^x = e^2x

d/dx ye^x = e^2x

ye^x = ∫ e^2x dx

.........= 1/2 e^2x + C

y = 1/2 e^x + C

the problem here, i didn't get the answer given which is..

y = 1/2 (e^x + e^-x)