What is the solution for y^'+3/4 y=1-t/3 ?

The solution for y^'+3/4 y=1-t/3 is y= 4/3-(4(3t-4)}{27}+(c_{1})/(e^{\frac{3t)/4)}

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y^'+3/4 y=1-t/3

y^{^{'}} + \frac{3}{4} y = 1 - \frac{t}{3}

y = \frac{4}{3} - \frac{4 ( 3 t - 4 )}{27} + \frac{c _{1}}{e ^{\frac{3 t}{4}}}

Solution steps

y^{'} (t) + \frac{3}{4} y = 1 - \frac{t}{3}

Solve linear ODE:

y = \frac{4}{3} - \frac{4 ( 3 t - 4 )}{27} + \frac{c _{1}}{e ^{\frac{3 t}{4}}}

y = \frac{4}{3} - \frac{4 ( 3 t - 4 )}{27} + \frac{c _{1}}{e ^{\frac{3 t}{4}}}

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What is the solution for y^'+3/4 y=1-t/3 ?
The solution for y^'+3/4 y=1-t/3 is y= 4/3-(4(3t-4)}{27}+(c_{1})/(e^{\frac{3t)/4)}