Question

verify that y=e^-x is a solution to the differential equation 3y'+4y=e^-x

Answer 1

Hey Val, welcome to OpenStudy!

When they say verify, they want you to plug it into the equation.
Do you understand how to find y'?

Answer 2

\[\large\rm \color{orangered}{y=e^{-x}}\qquad\qquad\qquad \color{royalblue}{y'=?}\]
\[\large\rm 3\color{royalblue}{y'}+4\color{orangered}{y}=e^{-x}\]\[\large\rm 3\color{royalblue}{y'}+4\color{orangered}{e^{-x}}=e^{-x}\]@vval25