**Unformatted text preview: **22 1 Solutions 16. The given equation is in standard form,
, an antiderivative is
, and the integrating factor is
. Now multiply by the
integrating factor to get
, the left hand side of which is a
perfect derivative
. Thus
and taking antiderivatives of
both sides gives
where
is a constant. Now multiply by
to get
for the general solution.
17. The given equation is in standard form,
,
tive is
, and the integrating factor is
by the integrating factor to get
of which is a perfect derivative
. Thus
antiderivatives of both sides gives where is a constant. Now multiply by , an antideriva. Now multiply
, the left hand side
and taking to get for the general solution.
18. The given diﬀerential equation is in standard form,
, an antiderivative is
, and the integrating factor is
. Now
multiply by the integrating factor to get
, the left
hand side of which is a perfect derivative
. Thus
.
Now assume
. Then taking antiderivatives of both sides gives
where
is a constant. Now multiply by
to
get
for the general solution. If
antiderivatives leads to
and hence
the general solution in this case. then taking
is 19. In standard form we get
. In this case
, an antiderivative is
, and the integrating factor
is
. Now multiply by the integrating factor to get
, the left hand side of which is a perfect derivative
. Thus
and taking antiderivatives of both
sides gives
where
is a constant. Now multiply by
and we get
for the general solution.
20. Divide by to put the equation in the standard form In this case
grating factor is
get , an antiderivative is
, and the inte. Now multiply by the integrating factor to ...

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