Integrating t(cost?)e-t"dt using integration by parts with the appropriate choice of u and dv. Which of the following options is true? ® Stccost³)e=f°at = - cost³) e-t* - Stsint?)e- t 1 (cost?) e-t - St(sint?)e-t°dt A ® St(cosr³)e-t*at = (sint") e- + fttcost?)e-t°dat 2 © St(cost?)e-t°dt = -2(cost?) e¬t² - St(sint²)e¬t°dt © S«cosr²)e-tat = 2(sint²) e-* + St(cost³)e-*at 2(sint?) e-t + [t(cost?)e- dt

Q: Find d^2y/dx^2 as a function of t, for the given  parameteric equations written below show all work…

A: From the parametric equation, the derivative dy/dx can be calculated as follows.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.