Exercise · ZW-FIRST-ORDER-LINEAR-EQUATION-004 · ★☆☆ Basic
The equation \(x\,y'+2y=x^2\), with \(x>0\), is brought to standard form by dividing by \(x\). What is \(p(x)\)?
Choose one option.
Show answer
- C. \(p(x)=\frac{2}{x}\)
Explanation
Dividing by \(x\) gives \(y'+\frac{2}{x}y=x\), so \(p=2/x\) and \(q=x\). Standard form requires coefficient 1 on \(y'\).
Review the concept: First-order linear equation
A first-order linear equation is a differential equation in which \(y\) and \(y'\) appear to the first power, with a coefficient \(p\) and a free term \(q\) that depend only on \(x\).
\[y'+p(x)\,y=q(x)\]
More practice problems: first-order linear equation
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- ZW-FIRST-ORDER-LINEAR-EQUATION-006 Find the general solution of y'+2xy=0.
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- ZW-FIRST-ORDER-LINEAR-EQUATION-008 Which of these functions is a solution of y'+y=x?
- ZW-FIRST-ORDER-LINEAR-EQUATION-009 The general solution of y'+y=x is y=x-1+Ce^-x. Which is the solution with y(0)=0?
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