What is the solution for (dN)/(dt)+N=Nt*e^{t+2} ?

The solution for (dN)/(dt)+N=Nt*e^{t+2} is N=e^{e^2(e^tt-e^t)-t+c_{1}}

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(dN)/(dt)+N=Nt*e^{t+2}

\frac{d N}{d t} + N = Nt \cdot e^{t + 2}

N = e^{e^{2} (e^{t} t - e^{t}) - t + c_{1}}

Solution steps

\frac{d N}{d t} + N = Nt \cdot e^{t + 2}

Solve separable ODE:

N = e^{e^{2} (e^{t} t - e^{t}) - t + c_{1}}

N = e^{e^{2} (e^{t} t - e^{t}) - t + c_{1}}

What is the solution for (dN)/(dt)+N=Nt*e^{t+2} ?
The solution for (dN)/(dt)+N=Nt*e^{t+2} is N=e^{e^2(e^tt-e^t)-t+c_{1}}