What is the solution for t(dQ)/(dt)+Q=t^5ln(t) ?

The solution for t(dQ)/(dt)+Q=t^5ln(t) is Q=(t^5ln(t))/6-(t^5}{36}+\frac{c_{1})/t

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t(dQ)/(dt)+Q=t^5ln(t)

t \frac{d Q}{d t} + Q = t^{5} ln (t)

Q = \frac{t ^{5} ln ( t )}{6} - \frac{t ^{5}}{36} + \frac{c _{1}}{t}

Solution steps

t \frac{d Q}{d t} + Q = t^{5} ln (t)

Solve linear ODE:

Q = \frac{t ^{5} ln ( t )}{6} - \frac{t ^{5}}{36} + \frac{c _{1}}{t}

Q = \frac{t ^{5} ln ( t )}{6} - \frac{t ^{5}}{36} + \frac{c _{1}}{t}

\int \frac{3}{1 + 2 e ^{x} - e ^{- x}} d x

t \to - 1 lim (t^{2} - x^{2})

\int \frac{( x e ^{x} )}{( 1 + x ) ^{2}} d x

\frac{\partial}{\partial z} (z - x)

What is the solution for t(dQ)/(dt)+Q=t^5ln(t) ?
The solution for t(dQ)/(dt)+Q=t^5ln(t) is Q=(t^5ln(t))/6-(t^5}{36}+\frac{c_{1})/t