Exercise · ZW-INITIAL-VALUE-PROBLEM-004 · ★☆☆ Basic
Solve \(y'=\cos x,\ y(0)=1\).
Choose one option.
Show answer
- D. \(y=\sin x+1\)
Explanation
Integrating, \(y=\sin x+C\); since \(\sin 0=0\), \(C=1\).
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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