CAIE Further Paper 2 2022 June — Question 3

Exam BoardCAIE
ModuleFurther Paper 2 (Further Paper 2)
Year2022
SessionJune
TopicSecond order differential equations

3 The variables \(t\) and \(x\) are related by the differential equation $$\frac { d ^ { 2 } x } { d t ^ { 2 } } + \frac { d x } { d t } + x = t ^ { 2 } + 1$$
  1. Find the general solution for \(x\) in terms of \(t\).
  2. Deduce an approximate value of \(\frac { \mathrm { d } ^ { 2 } \mathrm { x } } { \mathrm { dt } ^ { 2 } }\) for large positive values of \(t\).