Exercise · ZW-ORDER-AND-LINEARITY-003 · ★☆☆ Basic
Which of the following equations is linear?
Choose one option.
Show answer
- B. \(y''+xy'+y=e^x\)
Explanation
Only in \(y''+xy'+y=e^x\) do \(y\), \(y'\) and \(y''\) appear to the first power, with no products among them.
Review the concept: Order and linearity
The order of a differential equation is that of its highest derivative; the equation is linear if the unknown and its derivatives appear only to the first power and are never multiplied together.
\[a_n(x)\,y^{(n)}+\cdots+a_1(x)\,y'+a_0(x)\,y=g(x)\]
More practice problems: order and linearity
- ZW-ORDER-AND-LINEARITY-001 What is the order of y'''+2y'=x?
- ZW-ORDER-AND-LINEARITY-002 What is the order of (y')^3+y=0?
- ZW-ORDER-AND-LINEARITY-004 Which of the following equations is NOT linear?
- ZW-ORDER-AND-LINEARITY-005 What is the order of (y'')^2+y'=x?
- ZW-ORDER-AND-LINEARITY-006 Classify x^2y''+e^xy'+y=0:
- ZW-ORDER-AND-LINEARITY-007 Classify y''+y y'=0:
- ZW-ORDER-AND-LINEARITY-008 For which values of n is y'+y=y^n linear?
- ZW-ORDER-AND-LINEARITY-009 In a linear equation, the coefficients of y,y',dots may depend on: