Exercise · ZW-INITIAL-VALUE-PROBLEM-005 · ★★☆ Intermediate
Which function solves \(y'=y,\ y(1)=e\)?
Choose one option.
Show answer
- A. \(y=e^{x}\)
Explanation
With \(y=Ce^{x}\) the condition gives \(Ce=e\), so \(C=1\) and \(y=e^{x}\). The others fail the condition or the equation.
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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