Exercise · ZW-INITIAL-VALUE-PROBLEM-007 · ★★☆ Intermediate
If \(y'=-2y\) and \(y(0)=1\), what is \(y(\ln 2)\)?
Choose one option.
Show answer
- B. \(\tfrac14\)
Explanation
The solution is \(y=e^{-2x}\), and \(e^{-2\ln 2}=2^{-2}=\tfrac14\).
Review the concept: Initial value problem
An initial value problem asks for the solution of a differential equation that, in addition, takes given values at a given point.
\[y'=f(x,y),\qquad y(x_0)=y_0\]
More practice problems: initial value problem
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