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Homework Statement
$$\frac{dy}{dx}+y=\left\{\begin{matrix}1, \ 0\leq x< 1
\\
0, \ x\ge1 \ \ \ \ \ \ \
\end{matrix}\right.$$
Homework Equations
The Attempt at a Solution
$$P(x)=1$$
Integrating factor ##=e^{x}##
For ##f(x)=1##:
$$\frac{d}{dx}[e^{x}y]=e^{x}$$
Integrating both sides:
$$e^{x}y=e^{x}+C$$
$$y=1+\frac{C}{e^{x}}, y(0)=1$$
$$C=0$$
$$\fbox{y=1}$$
For ##f(x)=0##:
$$\frac{d}{dx}[e^{x}y]=0$$
Integrating both sides:
$$e^{x}y=C$$
$$y=\frac{C}{e^{x}}, y(0)=1$$
$$C=1$$
##y=\frac{1}{e^{x}}## <-- This one is coming back incorrect
I have worked through this problem multiple times, but my WeBWorK assignment keeps saying the second solution, the one for ##f(x)=0## is incorrect. I can't figure out what I'm doing wrong?! Any help would be greatly appreciated!