Determine if the given function y = f(x) is a solution of the accompanying differential equation.
-$$\begin{array} { l }
y ^ { \prime } = - y ^ { 2 } \
y = \frac { 1 } { x + 8 }
\end{array}$$

Question

Determine if the given function y = f(x) is a solution of the accompanying differential equation.
-$$\begin{array} { l } 
y ^ { \prime } = - y ^ { 2 } \
y = \frac { 1 } { x + 8 }
\end{array}$$

Quizplus · Accepted Answer

To check if the given function is a solution of the differential equation, we need to substitute it into the equation and see if it satisfies the equation.

Taking the derivative of y with respect to x, we get:

$y' = \frac{-1}{(x+8)^2}$

Now, substituting y and y' into the differential equation, we get:

$\frac{-1}{(x+8)^2} = -\left(\frac{1}{x+8}\right)^2$

Simplifying this equation, we get:

$\frac{-1}{(x+8)^2} = \frac{-1}{(x+8)^2}$

Both sides are equal, which means that the given function y = $\frac{1}{x+8}$ is indeed a solution of the differential equation. Therefore, the answer is A.

Determine If the Given Function Y = F(x) Is a Solution