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MMLU-Pro / 8534 / Consider the initial value problem

Problem

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

question

Consider the initial value problem $$ y^{\prime}=t y(4-y) / 3, \quad y(0)=y_0 $$ Suppose that y0=0.5y_0=0.5. Find the time TT at which the solution first reaches the value 3.98.
Plain-text mathematical notation (without MathML)
Consider the initial value problem
$$
y^{\prime}=t y(4-y) / 3, \quad y(0)=y_0
$$
Suppose that y₀=0.5. Find the time T at which the solution first reaches the value 3.98.
Original LaTeX notation
Consider the initial value problem
$$
y^{\prime}=t y(4-y) / 3, \quad y(0)=y_0
$$
Suppose that $y_0=0.5$. Find the time $T$ at which the solution first reaches the value 3.98.

category

math

options

  1. 3.01012
  2. 4.65218
  3. 5.12345
  4. 2.54678
  5. 3.87540
  6. 4.20456
  7. 3.29527
  8. 6.78901
  9. 2.75984
  10. 2.98732

src

scibench-diff

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Source and history

upstream_id / Original problem ID
8534
task_id
0972ca73-1485-55e2-82e3-a0a7c54ee52d
task_key
default--test--8534
task_revision_id
1
config / split
default / test

Official source

initial import