how to convert following second order ode into a system of first order ODEs

Question ; Convert following second order ode into a system of first order ODEs \[\frac{d^2y}{dt^2}+\frac{dy}{dt}+y=2t+3\sin{\left(t\right)} , y\left(0\right)=2,\ y^\prime\left(0\right)=3 \]Solution :Given second order ODE \[\frac{d^2y}{dt^2}+\frac{dy}{dt}+y=2t+3\sin{\left(t\right)} \] (1) Subject to intial conditions \[\ \ y\left(0\right)=2,\ y^\prime\left(0\right)=3\] To convert it into a system…

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