What is the solution for y^'-y=9te^{2t},y(0)=1 ?

The solution for y^'-y=9te^{2t},y(0)=1 is y=9e^{2t}(t-1)+10e^t

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y^'-y=9te^{2t},y(0)=1

y^{^{'}} - y = 9 t e^{2 t}, y (0) = 1

y = 9 e^{2 t} (t - 1) + 10 e^{t}

Solution steps

y^{'} (t) - y = 9 t e^{2 t}

Solve linear ODE:

y = 9 e^{2 t} (t - 1) + 10 e^{t}

y = 9 e^{2 t} (t - 1) + 10 e^{t}

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f (x) = x, g (x) = 2, h (x) = x

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What is the solution for y^'-y=9te^{2t},y(0)=1 ?
The solution for y^'-y=9te^{2t},y(0)=1 is y=9e^{2t}(t-1)+10e^t