Unformatted text preview: 1 Solutions 23 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
for the general solution. and we get 21. 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
and taking antiderivatives of both sides gives
where
is a constant. Now multiply by
to and we get
for the general solution.
22. 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
.
Taking antiderivatives of both sides and using integration by parts gives
where
is a constant. Now multiply
by
to get
for the general solution. Letting
gives
so
and 23. Divide by to put the equation in the standard form In this case
, an antiderivative is
, and the
integrating factor is
. Now multiply the standard form equation
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. Letting
gives
so
and ...
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 Fall '08
 BELL,D
 Derivative, Fundamental Theorem Of Calculus, Standard form, general solution

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