What is the solution for (dN)/(dt)+N=Nte^{t+3} ?

The solution for (dN)/(dt)+N=Nte^{t+3} is N=e^{e^{3+t}t-e^{3+t}-t+c_{1}}

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(dN)/(dt)+N=Nte^{t+3}

\frac{d N}{d t} + N = Nt e^{t + 3}

N = e^{e^{3 + t} t - e^{3 + t} - t + c_{1}}

Solution steps

\frac{d N}{d t} + N = Nt e^{t + 3}

Solve separable ODE:

N = e^{e^{3 + t} t - e^{3 + t} - t + c_{1}}

N = e^{e^{3 + t} t - e^{3 + t} - t + c_{1}}

5 x + 6

x + y

\int \frac{1 - x}{1 + x} d x

\frac{1}{2 x} + \frac{1}{3 x ^{\frac{2}{3}}}

\frac{d}{d x} (\frac{8 x ^{3} - 6 x ^{2}}{x ^{2} + 3 x - 2})

What is the solution for (dN)/(dt)+N=Nte^{t+3} ?
The solution for (dN)/(dt)+N=Nte^{t+3} is N=e^{e^{3+t}t-e^{3+t}-t+c_{1}}