The differential equation $y ^ { \prime } + y / x = y ^ { 2 }$ can be solved using the substitution
A) $u = y$
B) $u = y ^ { 2 }$
C) $u = y ^ { 3 }$
D) $u = y ^ { - 1 }$
E) $u = y ^ { - 2 }$

Question

Quizplus · Accepted Answer

The substitution $u = y^{-1}$ simplifies the given differential equation into a linear form, making it solvable. This is because differentiating $u = y^{-1}$ with respect to $x$ introduces a term that can cancel out the $y^2$ term in the original equation, leading to a simpler equation.

The Differential Equation y′+y/x=y2y ^ { \prime } + y / x = y ^ { 2 }y′+y/x=y2

The Differential Equation $y ^ { \prime } + y / x = y ^ { 2 }$