MATH 220 Lecture Notes - Lecture 2: Integrating Factor, Solution Process, Product Rule

• School: University of Maryland
• Department: Mathematics
• Course: MATH 220
• Professor: Heyrim Cho

Document Summary

The first kind of differential equation we are going to look at is the linear, first order differential equation. These are equations of the following form: (cid:1856)(cid:1856)(cid:1872)+(cid:1858)(cid:4666)(cid:1872)(cid:4667)=(cid:1859)(cid:4666)(cid:1872)(cid:4667) If the equation doesn"t come in this form, we will have to make it into this form. There"s not much else to say so let"s start off with an example . Now let"s apply this process to our problem. Step 1: we rewrite the equation in its standard form. We move the variable on the right side over to the left side and move the constant over to the sight side. We see that f(t) is . 274. (cid:1856)(cid:1874)(cid:1856)(cid:1872)+. (cid:884)(cid:889)(cid:886)(cid:1874)=(cid:891). (cid:890) Step 2: because f(t) is . 274, we can find the integrating factor (cid:1873)(cid:4666)(cid:1872)(cid:4667). (cid:1873)(cid:4666)(cid:1872)(cid:4667)=(cid:1857) . 274 =(cid:1857). 274. Step 3: we multiply this (cid:1873)(cid:4666)(cid:1872)(cid:4667) by our standard equation and simplify. (cid:1857). 274(cid:1856)(cid:1874)(cid:1856)(cid:1872)+. (cid:884)(cid:889)(cid:886)(cid:1874)(cid:1857). 274=(cid:891). (cid:890)(cid:1857). 274 (cid:4666)(cid:1857). 274(cid:1874)(cid:4667) =(cid:891). (cid:890)(cid:1857). 274. Step 4: next, we need to integrate both sides.