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)