What is the solution for (dP)/(dt)+2tP=P+6t-3 ?

The solution for (dP)/(dt)+2tP=P+6t-3 is P=e^{t-t^2+c_{1}}+3

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(dP)/(dt)+2tP=P+6t-3

\frac{d P}{d t} + 2 tP = P + 6 t - 3

P = e^{t - t^{2} + c_{1}} + 3

Solution steps

\frac{d P}{d t} + 2 tP = P + 6 t - 3

Solve separable ODE:

P = e^{t - t^{2} + c_{1}} + 3

P = e^{t - t^{2} + c_{1}} + 3

\int \frac{2 x + 5}{16 - 6 x - x ^{2}} d x

\int x^{3} x^{2} + 31 d x

x \to 0 lim (I n (x))

\int_{- 2}^{3} (x - 6) - (x^{2} - 12) d x

x \to 1 lim (\frac{8}{x ^{3} - 1})

What is the solution for (dP)/(dt)+2tP=P+6t-3 ?
The solution for (dP)/(dt)+2tP=P+6t-3 is P=e^{t-t^2+c_{1}}+3