Solve the differential equation.
-$$y ^ { \prime } - y = - x y ^ { 2 }$$
A) $x + 1 + C$
B) $\frac { e ^ { x } } { e ^ { x } ( x - 1 ) + C }$
C) $x - 1 + C$
D) $\frac { e ^ { x } } { ( x + 1 ) + C }$

Question

Quizplus · Accepted Answer

This differential equation is a first-order nonlinear ordinary differential equation that can be solved using an integrating factor or by recognizing it as a Bernoulli's equation. The correct solution involves transforming it into a linear equation through a substitution or directly integrating after rearranging, leading to the solution $\frac { e ^ { x } } { e ^ { x } ( x - 1 ) + C }$.

Solve the Differential Equation y′−y=−xy2y ^ { \prime } - y = - x y ^ { 2 }y′−y=−xy2

Solve the Differential Equation $y ^ { \prime } - y = - x y ^ { 2 }$