for One solution of this differential equation is Using this information, what is the general solution of the DE?
y(t) = ?
for One solution of this differential equation is Using this information, what is the general solution of the DE?
y(t) = ?
The general solution of the 'incomplete equation' $\displaystyle y^{'} + y =0$ is $\displaystyle y_{g}(t)= c\cdot e^{-t}$. The particular solution of the 'complete equation' $\displaystyle y^{'} + y = t$ You know is $\displaystyle y_{p} (t) = e^{-t} + t -1$, so that the general solution of the 'complete equation' is...
$\displaystyle y(t)=y_{g} (t) + y_{p} (t)= (1+c)\cdot e^{-t} + t -1$
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$\displaystyle \chi$ $\displaystyle \sigma$