Exercise · ZW-INITIAL-VALUE-PROBLEM-001 · ★☆☆ Basic
Solve \(y'=2y,\ y(0)=3\).
Choose one option.
Show answer
- B. \(y=3e^{2x}\)
Explanation
The general solution is \(y=Ce^{2x}\); with \(y(0)=C=3\) we get \(y=3e^{2x}\).
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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- ZW-INITIAL-VALUE-PROBLEM-007 If y'=-2y and y(0)=1, what is y(ln 2)?
- ZW-INITIAL-VALUE-PROBLEM-008 Solve y''=6x with y(0)=1 and y'(0)=2.
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