Exercise · ZW-INITIAL-VALUE-PROBLEM-006 · ★★☆ Intermediate
If \(y'=3x^2\) and \(y(1)=2\), what is \(y(2)\)?
Choose one option.
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- C. 9
Explanation
Integrating, \(y=x^3+C\); \(2=1+C\) gives \(C=1\), so \(y(2)=8+1=9\).
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.
\[y'=f(x,y),\qquad y(x_0)=y_0\]
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