What is the solution for (dN)/(dt)+N=Nte^{t+5} ?

The solution for (dN)/(dt)+N=Nte^{t+5} is N=e^{e^{5+t}t-e^{5+t}-t+c_{1}}

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(dN)/(dt)+N=Nte^{t+5}

\frac{d N}{d t} + N = Nt e^{t + 5}

N = e^{e^{5 + t} t - e^{5 + t} - t + c_{1}}

Solution steps

\frac{d N}{d t} + N = Nt e^{t + 5}

Solve separable ODE:

N = e^{e^{5 + t} t - e^{5 + t} - t + c_{1}}

N = e^{e^{5 + t} t - e^{5 + t} - t + c_{1}}

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t \to 0 lim (3 t^{2})

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What is the solution for (dN)/(dt)+N=Nte^{t+5} ?
The solution for (dN)/(dt)+N=Nte^{t+5} is N=e^{e^{5+t}t-e^{5+t}-t+c_{1}}