Category: 0. BLOG

For the system x′ = 3x + 4y, y′ = −4x + 3y, the eigenvalues of A are A 3

For a linear system dX/dt = AX, if A has two distinct real eigenvalues, the solution is generally A Pure

If a coupled linear system is written as dX/dt = AX, the usual solution idea uses A Only separation B

In a coupled system where dx/dt depends on both x and y, the system is called A Single separable ODE

A “simultaneous differential equation” usually means A One separable ODE B One exact ODE C Two coupled ODEs D One

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