What is the solution for tln(t)(dr)/(dt)+r=9te^t ?

The solution for tln(t)(dr)/(dt)+r=9te^t is r=(9e^t)/(ln(t))+(c_{1})/(ln(t))

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tln(t)(dr)/(dt)+r=9te^t

t ln (t) \frac{d r}{d t} + r = 9 t e^{t}

r = \frac{9 e ^{t}}{ln ( t )} + \frac{c _{1}}{ln ( t )}

Solution steps

t ln (t) \frac{d r}{d t} + r = 9 t e^{t}

Solve linear ODE:

r = \frac{9 e ^{t}}{ln ( t )} + \frac{c _{1}}{ln ( t )}

r = \frac{9 e ^{t}}{ln ( t )} + \frac{c _{1}}{ln ( t )}

\frac{d}{d x} ((\frac{x - 9}{x + 2})^{\frac{3}{2}})

f (x) = - 9 x^{\frac{1}{3}} + 5, at x = 27

x \to \infty lim (\frac{7}{x} - 9)

\int 45 x^{2} ln (x) d x

\frac{d}{d x} (\frac{x}{9})

What is the solution for tln(t)(dr)/(dt)+r=9te^t ?
The solution for tln(t)(dr)/(dt)+r=9te^t is r=(9e^t)/(ln(t))+(c_{1})/(ln(t))