What is the solution for 6t((dy)/(dt))+5y=sqrt(t) ?

The solution for 6t((dy)/(dt))+5y=sqrt(t) is y=(t^{1/2})/8+(c_{1})/(t^{5/6)}

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6t((dy)/(dt))+5y=sqrt(t)

6 t (\frac{d y}{d t}) + 5 y = t

y = \frac{t ^{\frac{1}{2}}}{8} + \frac{c _{1}}{t ^{\frac{5}{6}}}

Solution steps

6 t (\frac{d y}{d t}) + 5 y = t

Solve linear ODE:

y = \frac{t ^{\frac{1}{2}}}{8} + \frac{c _{1}}{t ^{\frac{5}{6}}}

y = \frac{t ^{\frac{1}{2}}}{8} + \frac{c _{1}}{t ^{\frac{5}{6}}}

What is the solution for 6t((dy)/(dt))+5y=sqrt(t) ?
The solution for 6t((dy)/(dt))+5y=sqrt(t) is y=(t^{1/2})/8+(c_{1})/(t^{5/6)}