The singular points of $x ^ { 2 } ( x - 1 ) y ^ { \prime \prime } - 2 x y ^ { \prime } + y = 0$ are $x =$ Select all that apply.
A) 2
B) $- 1$
C) 0
D) 1
E) none of the above

Question

Quizplus · Accepted Answer

Singular points occur where the coefficient of the highest derivative becomes zero, making the equation non-linear. For the given differential equation, $x^2(x-1)y''$, the coefficient is $x^2(x-1)$. This becomes zero at $x = 0$ and $x = 1$, making these the singular points.

The Singular Points Of x2(x−1)y′′−2xy′+y=0x ^ { 2 } ( x - 1 ) y ^ { \prime \prime } - 2 x y ^ { \prime } + y = 0x2(x−1)y′′−2xy′+y=0

The Singular Points Of $x ^ { 2 } ( x - 1 ) y ^ { \prime \prime } - 2 x y ^ { \prime } + y = 0$