What is the solution for y^'+4/5 y=1-1/4 t,y(0)=0 ?

The solution for y^'+4/5 y=1-1/4 t,y(0)=0 is y=(5(-4t+21)}{64}-(105)/(64e^{\frac{4t)/5)}

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y^'+4/5 y=1-1/4 t,y(0)=0

y^{^{'}} + \frac{4}{5} y = 1 - \frac{1}{4} t, y (0) = 0

y = \frac{5 ( - 4 t + 21 )}{64} - \frac{105}{64 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{105}{64 e ^{\frac{4 t}{5}}}

y = \frac{5 ( - 4 t + 21 )}{64} - \frac{105}{64 e ^{\frac{4 t}{5}}}

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What is the solution for y^'+4/5 y=1-1/4 t,y(0)=0 ?
The solution for y^'+4/5 y=1-1/4 t,y(0)=0 is y=(5(-4t+21)}{64}-(105)/(64e^{\frac{4t)/5)}