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Mathematics
Problem
Consider the differential equation
y
′
+
y
=
x
e
x
y' + y = x e^{x}
y
′
+
y
=
x
e
x
. Which of the following functions is a solution? a)
x
2
e
x
\dfrac{x}{2}e^{x}
2
x
e
x
b)
2
x
−
1
4
e
x
\dfrac{2x-1}{4}e^{x}
4
2
x
−
1
e
x
c)
2
x
−
1
4
e
2
x
\dfrac{2x-1}{4}e^{2x}
4
2
x
−
1
e
2
x
d)
x
2
2
e
x
\dfrac{x^{2}}{2}e^{x}
2
x
2
e
x
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