find integrating factor and solve the equation 3

naspek

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)

vela

You made an algebra mistake in the last step when solving for y.

naspek

ok.. here is my mistake...
ye^x = ∫ e^2x dx
.........= 1/2 e^2x + C

so.. when am i going to solve C value?

vela

Up to there is correct. Your error was in the very last step you wrote when you solved for y.

You can solve for C any time you want. Most of the time, it's done as the final step.