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Update lecture-05.html
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jcponce committed Jul 31, 2023
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Expand Up @@ -208,18 +208,18 @@ <h5>1 Ordinary Differential Equations</h5>
<div class="left-txt">
<p>
<strong>Important remark: </strong>
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<span>
The final two steps will not always be possible.
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<span>
Whenever you are
asked to solve a separable ODE or IVP in this course you are supposed to always
"go as far as possible".
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<span>
For good reasons we assume you are infinitely smart;
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not being able to compute simple integrals is never a valid excuse.
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Expand All @@ -230,11 +230,11 @@ <h5>1 Ordinary Differential Equations</h5>
that we can't evaluate one of both of the integrals needed to solve the
separable ODE.
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In this case, we can still write down an actual solution, be it
a rather implicit one.
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<span class="fragment" data-fragment-index="4">
Indeed, the solution to the IVP is given by
\[
\int_{y_0}^y\frac{\dup t}{g(t)} = \int_{x_0}^x f(t) \dup t.
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