Separable Differential Equations

8/23 Lecture from Cochise College MAT 262. This lesson covers separable differential equations, and talks a bit about initial value problems and intervals of solution.

[@pagoeagle_4198]

🔥🔥🔥

[@goodshortvideos9647]

I didn't get the point at 59:03

[@patrickjones1510]

In general, a differential equation can have multiple solutions. However, often if you specify a value (or initial value) of the function for a given input, you can go further and find a unique solution.

[@goodshortvideos9647]

@@patrickjones1510 I'm having a problem with the last sentence you said " you can go further and find a unique solution" .....

[@patrickjones1510]

@@goodshortvideos9647 When you integrate both sides, you get a generic +c involved. Because we have the initial value that y(0)=5/2, we can use that to find the actual particular value of c that makes the IVP work. You can think of y(0)=5/2 as "when t=0, it must be that y=5/2," and plug those values into the equation. Then the only unknown is c, and we solve for it.

[@goodshortvideos9647]

thank you very much for the lecture and the explanation @@patrickjones1510