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MMLU-Pro / 7991 / Consider the initial value problem (see Example 5)

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Consider the initial value problem (see Example 5) $$ y^{\prime \prime}+5 y^{\prime}+6 y=0, \quad y(0)=2, \quad y^{\prime}(0)=\beta $$ where β>0\beta>0. Determine the smallest value of β\beta for which ym≥4y_m \geq 4.
Plain-text mathematical notation (without MathML)
Consider the initial value problem (see Example 5)
$$
y^{\prime \prime}+5 y^{\prime}+6 y=0, \quad y(0)=2, \quad y^{\prime}(0)=\beta
$$
where β>0.
Determine the smallest value of β for which y_(m)≥4.
Original LaTeX notation
Consider the initial value problem (see Example 5)
$$
y^{\prime \prime}+5 y^{\prime}+6 y=0, \quad y(0)=2, \quad y^{\prime}(0)=\beta
$$
where $\beta>0$.
Determine the smallest value of $\beta$ for which $y_m \geq 4$.

category

math

options

  1. 17.3891
  2. 16.3923
  3. 18.2765
  4. 13.1789
  5. 14.2507
  6. 21.7432
  7. 20.4521
  8. 19.5678
  9. 15.3298
  10. 22.8915

src

scibench-diff

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Source and history

upstream_id / Original problem ID
7991
task_id
d00266d6-533e-54e1-a56f-a79fce13e43d
task_key
default--test--7991
task_revision_id
1
config / split
default / test

Official source

initial import