Initial Value Problem: f'(x) = e^x - 2x, f(0) = 2

[Jade]

Find function f(x) by solving the initial Value problem (IVP):

. . .f'(x) = e^x - 2x
. . .f(0) = 2

I believe I need to find the anti-derivative, this is what I have so far:

. . .f(x) = e^x - x^2 + c
. . .f(x) = e^x - x^2 + 2

 

[Unco]

Re: Initial Value Problem

Find function f(x) by solving the initial Value problem (IVP)
f'(x)=e^x-2x
f(0)=2

I believe I need to find the anti-derivative, this is what I have so far

f(x)=e^x-x^2+c
Good, Jade, now to find c:
f(0) = e^0 - 0^2 + c = 1 + c
and you know f(0)=2.

 

[Jade]

c=1

So c=1

so the answer is actually f(x)=e^x-x^2+1???