What is the solution for ty^'+7y=t^2-t+1,y(1)= 1/7 ?

The solution for ty^'+7y=t^2-t+1,y(1)= 1/7 is y=(t^2)/9-t/8+1/7+1/(72t^7)

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ty^'+7y=t^2-t+1,y(1)= 1/7

t y^{^{'}} + 7 y = t^{2} - t + 1, y (1) = \frac{1}{7}

y = \frac{t ^{2}}{9} - \frac{t}{8} + \frac{1}{7} + \frac{1}{72 t ^{7}}

Solution steps

t y^{'} (t) + 7 y = t^{2} - t + 1

Solve linear ODE:

y = \frac{t ^{2}}{9} - \frac{t}{8} + \frac{1}{7} + \frac{1}{72 t ^{7}}

y = \frac{t ^{2}}{9} - \frac{t}{8} + \frac{1}{7} + \frac{1}{72 t ^{7}}

What is the solution for ty^'+7y=t^2-t+1,y(1)= 1/7 ?
The solution for ty^'+7y=t^2-t+1,y(1)= 1/7 is y=(t^2)/9-t/8+1/7+1/(72t^7)