What is the solution for y^'+4/5 y=1-1/4 t ?

The solution for y^'+4/5 y=1-1/4 t is y=(5(-4t+21)}{64}+(c_{1})/(e^{\frac{4t)/5)}

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y^'+4/5 y=1-1/4 t

y^{^{'}} + \frac{4}{5} y = 1 - \frac{1}{4} t

y = \frac{5 ( - 4 t + 21 )}{64} + \frac{c _{1}}{e ^{\frac{4 t}{5}}}

Solution steps

y^{'} (t) + \frac{4}{5} y = 1 - \frac{1}{4} t

Solve linear ODE:

y = \frac{5 ( - 4 t + 21 )}{64} + \frac{c _{1}}{e ^{\frac{4 t}{5}}}

y = \frac{5 ( - 4 t + 21 )}{64} + \frac{c _{1}}{e ^{\frac{4 t}{5}}}

What is the solution for y^'+4/5 y=1-1/4 t ?
The solution for y^'+4/5 y=1-1/4 t is y=(5(-4t+21)}{64}+(c_{1})/(e^{\frac{4t)/5)}