What is the solution for y^'-y=6te^{2t},y(0)=1 ?

The solution for y^'-y=6te^{2t},y(0)=1 is y=6e^{2t}(t-1)+7e^t

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y^'-y=6te^{2t},y(0)=1

y^{^{'}} - y = 6 t e^{2 t}, y (0) = 1

y = 6 e^{2 t} (t - 1) + 7 e^{t}

Solution steps

y^{'} (t) - y = 6 t e^{2 t}

Solve linear ODE:

y = 6 e^{2 t} (t - 1) + 7 e^{t}

y = 6 e^{2 t} (t - 1) + 7 e^{t}

x \to 0 lim (x^{2} \cdot e^{- x})

\frac{d}{d x} (\frac{1}{3} x^{\frac{3}{2}} - x^{\frac{1}{2}})

\frac{d y}{d x} + 6 y = 9

\int_{0}^{5} x^{2} (x - 5)^{4} d x

x \to 2 lim (\frac{x - 2}{x ^{3} - 8})

What is the solution for y^'-y=6te^{2t},y(0)=1 ?
The solution for y^'-y=6te^{2t},y(0)=1 is y=6e^{2t}(t-1)+7e^t