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Mathematics
Problem
Which differential equation can be solved by rewriting the right–hand side as a sum of simple rational functions with distinct linear factors of
x
x
x
only? a)
d
y
d
x
=
3
x
(
x
−
2
)
2
\displaystyle \frac{dy}{dx}=\frac{3x}{(x-2)^{2}}
d
x
d
y
=
(
x
−
2
)
2
3
x
b)
d
y
d
x
=
sin
x
x
2
+
1
\displaystyle \frac{dy}{dx}=\frac{\sin x}{x^{2}+1}
d
x
d
y
=
x
2
+
1
sin
x
c)
d
y
d
x
=
2
x
+
3
x
(
x
−
5
)
\displaystyle \frac{dy}{dx}=\frac{2x+3}{x(x-5)}
d
x
d
y
=
x
(
x
−
5
)
2
x
+
3
d)
d
y
d
x
=
2
x
+
1
(
x
−
3
)
(
x
2
+
1
)
\displaystyle \frac{dy}{dx}=\frac{2x+1}{(x-3)(x^{2}+1)}
d
x
d
y
=
(
x
−
3
)
(
x
2
+
1
)
2
x
+
1
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