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

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

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

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

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

Solution steps

\frac{d N}{d t} + N = N \cdot t 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}}

\frac{d y}{d x} = \frac{( y x + 5 x )}{x ^{2} + 1}

y^{^{'}} - 3 y sin (3 t) = - 3 sin (3 t), y (\frac{π}{6}) = 2

y^{^{'}} = \frac{y ^{2}}{4}

\frac{d P}{d t} = 0.015 P

\frac{d x}{d t} = 7 - x

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