Answer
$y=-2e^{6-6x}+5$
Work Step by Step
The characteristic equation for $y''+6y'=0$ is $t^2+6t=0$ with solutions $t=0$ and $t=-6$
The general solution is of the form: $c_1e^{-6x}+c_2$
As per question, $y(1)=3$ and $y'(1)=12$ after plugging in the values
We have $c_1=-2e^{6}$, $c_2=6$
Final result: $y=-2e^{6-6x}+5$
