What is the solution for (dN)/(dt)+N=Nte^{t+7} ?

The solution for (dN)/(dt)+N=Nte^{t+7} is N=e^{e^{7+t}t-e^{7+t}-t+c_{1}}

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(dN)/(dt)+N=Nte^{t+7}

\frac{d N}{d t} + N = Nt e^{t + 7}

N = e^{e^{7 + t} t - e^{7 + t} - t + c_{1}}

Solution steps

\frac{d N}{d t} + N = Nt e^{t + 7}

Solve separable ODE:

N = e^{e^{7 + t} t - e^{7 + t} - t + c_{1}}

N = e^{e^{7 + t} t - e^{7 + t} - t + c_{1}}

\int_{- 1}^{0} (2 x - 1) d x

f^{^{''}} (x) = - f (x), f (0) = 0, f^{^{'}} (0) = 1

n = 1 \sum \infty e^{- 6 n} - e^{- 6 (n + 1)}

\int (4 x - 3) 5 d x

\int_{- 2}^{6} 4 x - x^{2} - 12 d x

What is the solution for (dN)/(dt)+N=Nte^{t+7} ?
The solution for (dN)/(dt)+N=Nte^{t+7} is N=e^{e^{7+t}t-e^{7+t}-t+c_{1}}