13. differential equations

13.1 introduction to differential equations

• particular fractions: specific solution to a differentiated equation that does not depend on any unknown constants (graphs can share the same gradient, but have different equations),

• basically, using given conditions to solve for +c (DON’T FORGET +C),

13.2 separable differential equations

• to solve dy/dx = f(x) g(y)

  1. get all the x’s and y’s on opposite sides,

  2. separate dy/dx as if it were a fraction,

  3. integrate both sides (only one +c)

• when you take the e of something, everything goes to the power of one e

• e ^{ln something + ln something}, if something is in front of that ln (like a - or value), it needs to be moved e.g., taking it to the power, because you can’t cancel e ^ln if they are not directly next to each other.

• always take out the multiple before taking the ln.