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

Question

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

Quizplus · Accepted Answer

To verify if $y = e^{7x} + 7xe^{x}$ is a solution to the differential equation $y' - y = 7e^{x}$, we first find the derivative of $y$, which is $y' = 7e^{7x} + 7e^{x} + 7xe^{x}$. Substituting $y$ and $y'$ into the differential equation gives $7e^{7x} + 7e^{x} + 7xe^{x} - (e^{7x} + 7xe^{x}) = 7e^{x}$. Simplifying this does not yield a true statement, indicating that the given function is not a solution to the differential equation.

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