Exercise · ZW-INITIAL-VALUE-PROBLEM-008 · ★★☆ Intermediate
Solve \(y''=6x\) with \(y(0)=1\) and \(y'(0)=2\).
Choose one option.
Show answer
- D. \(y=x^3+2x+1\)
Explanation
Integrating twice, \(y=x^3+C_1x+C_2\); \(y'(0)=C_1=2\) and \(y(0)=C_2=1\).
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.
\[y'=f(x,y),\qquad y(x_0)=y_0\]
More practice problems: initial value problem
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- ZW-INITIAL-VALUE-PROBLEM-009 The solution of y'=y^2,\ y(0)=1 is y=(1)/(1-x). What is the largest interval containing 0 where it…
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