Author: Study Clue

For y1=eaxy1=eax and y2=ebxy2=ebx with a≠ba=b, the Wronskian equals A (a+b)e(a−b)x(a+b)e(a−b)x B 00 always C (b−a)e(a+b)x(b−a)e(a+b)x D (a−b)e(a+b)x(a−b)e(a+b)x Explanation W=y1y2′−y2y1′W=y1y2′−y2y1′.

For y1=sin⁡xy1=sinx and y2=cos⁡xy2=cosx, the Wronskian W(y1,y2)W(y1,y2) equals A 11 B 00 C −1−1 D sin⁡xsinx Explanation W=y1y2′−y2y1′W=y1y2′−y2y1′. Here y2′=−sin⁡xy2′=−sinx

For solutions of y′′+P(x)y′+Q(x)y=0y′′+P(x)y′+Q(x)y=0, Abel’s formula mainly helps you find A Particular integral B Laplace inverse C Wronskian form D

For two functions y1,y2y1,y2, the Wronskian W(y1,y2)W(y1,y2) is A y1+y2y1+y2 B A 2×2 determinant C y1y2y1y2 D y1/y2y1/y2 Explanation The

In second-order linear ODE theory, what is the Wronskian of two functions? A A determinant test B A derivative rule

Find order and degree ofleft(y′′′right)4+(y′′)3=0left(y′′′right)4+(y′′)3=0 A Order 4, Degree 3 B Order 3, Degree 4 C Order 3, Degree 3

Find order and degree of y′′′+(y′)4=0y′′′+(y′)4=0 A Order 1, Degree 4 B Order 4, Degree 3 C Order 3, Degree

Find order and degree of (y′′)3+y′=0(y′′)3+y′=0 A Order 3, Degree 2 B Order 2, Degree 1 C Order 2, Degree

Which part decides the order of a differential equation A Highest derivative order B Highest power only C Number of

Which statement best defines a differential equation A Equation with limits B Equation with derivatives C Equation with vectors D