What is the solution for 7t*(dy)/(dt)+3y=sqrt(t) ?

The solution for 7t*(dy)/(dt)+3y=sqrt(t) is y=(2t^{1/2})/(13)+(c_{1})/(t^{3/7)}

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7t*(dy)/(dt)+3y=sqrt(t)

7 t \cdot \frac{d y}{d t} + 3 y = t

y = \frac{2 t ^{\frac{1}{2}}}{13} + \frac{c _{1}}{t ^{\frac{3}{7}}}

Solution steps

7 t \cdot \frac{d y}{d t} + 3 y = t

Solve linear ODE:

y = \frac{2 t ^{\frac{1}{2}}}{13} + \frac{c _{1}}{t ^{\frac{3}{7}}}

y = \frac{2 t ^{\frac{1}{2}}}{13} + \frac{c _{1}}{t ^{\frac{3}{7}}}

\int \frac{2 e ^{2 x}}{e ^{2 x} + 14 e ^{x} + 48} d x

\int t^{3} 9 t^{4} + 1 d t

\frac{d y}{d x} = 3 x^{2} (1 + y^{2})

y^{^{'}} = \frac{4 x sec ( \frac{y}{x} ) + y}{x}

y^{^{''}} + π y = 0

What is the solution for 7t*(dy)/(dt)+3y=sqrt(t) ?
The solution for 7t*(dy)/(dt)+3y=sqrt(t) is y=(2t^{1/2})/(13)+(c_{1})/(t^{3/7)}