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Mathematics
Problem
Prove that
x
y
=
a
e
x
+
b
e
−
x
+
x
2
xy = ae^x + be^{-x} + x^2
x
y
=
a
e
x
+
b
e
−
x
+
x
2
is the general solution of the differential equation
x
d
2
y
d
x
2
+
2
d
y
d
x
−
x
y
+
x
2
−
2
=
0
x \frac{d^2y}{dx^2} + 2 \frac{dy}{dx} - xy + x^2 - 2 = 0
x
d
x
2
d
2
y
+
2
d
x
d
y
−
x
y
+
x
2
−
2
=
0
.
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