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 by reducing it to a linear form. By substituting $u = y^{-1}$, we get $y = u^{-1}$ and $y' = -u^{-2}u'$, which can be substituted back into the original equation to simplify it.

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

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