Chaotic Junkyard

The 2nd Order ODE is non-Linear in the form of: The intuitive solution is to convert it as a first-order ODE (still non-linear) with   It reduces into: By Separable: It could be solved by trigonometric substitution (using sine preferred) and result in: Remaking the subject: The integration could be done by the substitution: This makes the integral into: The integration could be solved easily by considering: Then the solution follows: Finalized:   #ODE #AirResistance

 Question paper: https://drive.google.com/file/d/1q2L8zJSRsLfpaupx38m5tU25EueB1lwT/view?usp=sharing #DSE #PastPaper #M2math

Question paper:  https://drive.google.com/file/d/1JMmsQcj8Qjn7fs3i1BAYH3wPAakudgPO/view?usp=sharing Marking Scheme: https://drive.google.com/file/d/1JMmsQcj8Qjn7fs3i1BAYH3wPAakudgPO/view?usp=sharing #HKDSE #PastPaper

How to solve a PDE – first order in the form of: Algorithm Solving it as if it is a ODE: Simultaneous ODE:  Solving the first equation results in:  Further solve the second equation results in: Final: Initial Values (if exists) Example This results in ODE: Solving: Initial Value #PDE #PartialDifferentialEquation