A-LevelFurther MathematicsDifferential equations9231/12 · Oct/Nov 2017 · Q26 Marks
Find the general solution of the differential equation d²x/dt² + 2dx/dt + 5x = 4 – 5t².
- Find the general solution of the differential equation d²x/dt² + 2dx/dt + 5x = 4 – 5t².[6]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [1] CF: m² + 2m + 5 = 0 ⇒ m = −1 ± 2i
- [1] e¯ᵗ(A cos 2t + B sin 2t)
- [1] PI: x = pt² + qt + r ⇒ ẋ = 2pt + q ⇒ ẍ = 2p
- [1] 2p + 4pt + 2q + 5pt² + 5qt + 5r = 4 – 5t²
- [1] ⇒ p = −1, q = 4/5, r = 22/25
- [1] GS: x = e¯ᵗ(A cos 2t + B sin 2t) + (4/5)t - t² + 22/25
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