Determine if the given function y = f(x) is a solution of the accompanying differential equation.
-$$\begin{array} { l }
y ^ { \prime } + y = e ^ { 2 x } \
y = 7 e ^ { - x } + \frac { 1 } { 3 } e ^ { 2 x }
\end{array}$$

Question

Determine if the given function y = f(x) is a solution of the accompanying differential equation.
-$$\begin{array} { l } 
y ^ { \prime } + y = e ^ { 2 x } \
y = 7 e ^ { - x } + \frac { 1 } { 3 } e ^ { 2 x }
\end{array}$$

Quizplus · Accepted Answer

To check whether the given function is a solution of the differential equation, we need to plug in the function and its derivative into the differential equation and check if the equation holds true.

Using the given function, we can find its derivative as:
$$ y' = -7e^{-x}+ \frac{2}{3}e^{2x} $$

Now, plugging in both the function and its derivative into the differential equation, we get:
$$ y' + y = (-7e^{-x}+ \frac{2}{3}e^{2x}) + (7 e^{-x} + \frac{1}{3}e^{2x}) = \frac{7}{3}e^{2x} $$

On the other hand, the right-hand side of the differential equation is given as $e^{2x}$. Since $\frac{7}{3}e^{2x} 
eq e^{2x}$, the given function is not a solution to the differential equation.

Therefore, the answer is B) False.

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