What is the solution for (dN)/(dt)+N=Nte^{t+6} ?

The solution for (dN)/(dt)+N=Nte^{t+6} is N=e^{e^{6+t}t-e^{6+t}-t+c_{1}}

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(dN)/(dt)+N=Nte^{t+6}

\frac{d N}{d t} + N = Nt e^{t + 6}

N = e^{e^{6 + t} t - e^{6 + t} - t + c_{1}}

Solution steps

\frac{d N}{d t} + N = Nt e^{t + 6}

Solve separable ODE:

N = e^{e^{6 + t} t - e^{6 + t} - t + c_{1}}

N = e^{e^{6 + t} t - e^{6 + t} - t + c_{1}}

\frac{d}{d x} (\frac{x - 6}{x + 6})

\int \frac{x ^{3}}{a} - \frac{a}{x ^{2}} d x

y = e^{x}, y = e^{2 x}, x = 0, x = ln (4)

\frac{\partial}{\partial y} (y^{x} - ln (x^{3} y + 6 x))

x \to - 4 + lim (\frac{- 6 x}{x + 4})

What is the solution for (dN)/(dt)+N=Nte^{t+6} ?
The solution for (dN)/(dt)+N=Nte^{t+6} is N=e^{e^{6+t}t-e^{6+t}-t+c_{1}}