Let f(t) be the solution to of $y ^ { \prime }$ = $y ^ { 2 }$ t - y, y(0) = 1. Which of the following statements is true?

Question

Quizplus · Accepted Answer

Given the differential equation $y' = y^2t - y$ and the initial condition $y(0) = 1$, we can evaluate the derivative at the origin. Substituting $t = 0$ and $y = 1$ into the differential equation gives $y' = (1)^2(0) - 1 = -1$, indicating that $f$ is decreasing at the origin.

Let F(t) Be the Solution to Of y′y ^ { \prime }y′

Let F(t) Be the Solution to Of $y ^ { \prime }$