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MMLU-Pro / 8640 / 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 $$ y^{\prime}+\frac{2}{3} y=1-\frac{1}{2} t, \quad y(0)=y_0 . $$ Find the value of y0y_0 for which the solution touches, but does not cross, the tt-axis.
Plain-text mathematical notation (without MathML)
Consider the initial value problem
$$
y^{\prime}+\frac{2}{3} y=1-\frac{1}{2} t, \quad y(0)=y_0 .
$$
Find the value of y₀ for which the solution touches, but does not cross, the t-axis.
Original LaTeX notation
Consider the initial value problem
$$
y^{\prime}+\frac{2}{3} y=1-\frac{1}{2} t, \quad y(0)=y_0 .
$$
Find the value of $y_0$ for which the solution touches, but does not cross, the $t$-axis.

category

math

options

  1. −1.642876
  2. -1.23456
  3. -3.14159
  4. -1.41421
  5. -1.73205
  6. -2.34567
  7. -2.71828
  8. 0
  9. -0.98765
  10. -2.00000

src

scibench-diff

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Source and history

upstream_id / Original problem ID
8640
task_id
e82efc3a-3718-52c3-a5f7-3eb7fbbc4814
task_key
default--test--8640
task_revision_id
1
config / split
default / test

Official source

initial import