The singular points of the differential equation $x y ^ { \prime \prime } + y ^ { \prime } + y ( x + 2 ) / ( x - 4 ) = 0$ are
A) none
B) 0
C) 0, $- 2$
D) 0, 4
E) 0, $- 2$ , 4

Question

Quizplus · Accepted Answer

Singular points occur where the coefficient of the highest derivative becomes zero or where the differential equation becomes undefined. In this equation, the term $x y''$ suggests $x = 0$ is a singular point because it would make the coefficient of $y''$ zero. Additionally, the term $(x + 2)/(x - 4)$ suggests $x = 4$ is a singular point because it would make the equation undefined (division by zero). Therefore, the singular points are $x = 0$ and $x = 4$.

The Singular Points of the Differential Equation xy′′+y′+y(x+2)/(x−4)=0x y ^ { \prime \prime } + y ^ { \prime } + y ( x + 2 ) / ( x - 4 ) = 0xy′′+y′+y(x+2)/(x−4)=0

The Singular Points of the Differential Equation $x y ^ { \prime \prime } + y ^ { \prime } + y ( x + 2 ) / ( x - 4 ) = 0$