What is the solution for y^'+6/5 y=1-1/6 t ?

The solution for y^'+6/5 y=1-1/6 t is y=(5(-6t+41)}{216}+(c_{1})/(e^{\frac{6t)/5)}

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y^'+6/5 y=1-1/6 t

y^{^{'}} + \frac{6}{5} y = 1 - \frac{1}{6} t

y = \frac{5 ( - 6 t + 41 )}{216} + \frac{c _{1}}{e ^{\frac{6 t}{5}}}

Solution steps

y^{'} (t) + \frac{6}{5} y = 1 - \frac{1}{6} t

Solve linear ODE:

y = \frac{5 ( - 6 t + 41 )}{216} + \frac{c _{1}}{e ^{\frac{6 t}{5}}}

y = \frac{5 ( - 6 t + 41 )}{216} + \frac{c _{1}}{e ^{\frac{6 t}{5}}}

f (x) = (x^{3} - 8)^{\frac{2}{3}}

y^{^{''}} + 81 y = cos (8 t)

e^{3} + 2

\int_{1}^{4} \frac{1}{x ^{2}} - \frac{8}{x ^{3}} d x

x^{^{'}} = x^{3}

What is the solution for y^'+6/5 y=1-1/6 t ?
The solution for y^'+6/5 y=1-1/6 t is y=(5(-6t+41)}{216}+(c_{1})/(e^{\frac{6t)/5)}