What is the solution for (dy)/(dt)=6y+te^{6t} ?

The solution for (dy)/(dt)=6y+te^{6t} is y=(t^2)/(2e^{-6t)}+c_{1}e^{6t}

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(dy)/(dt)=6y+te^{6t}

\frac{d y}{d t} = 6 y + t e^{6 t}

y = \frac{t ^{2}}{2 e ^{- 6 t}} + c_{1} e^{6 t}

Solution steps

\frac{d y}{d t} = 6 y + t e^{6 t}

Solve linear ODE:

y = \frac{t ^{2}}{2 e ^{- 6 t}} + c_{1} e^{6 t}

y = \frac{t ^{2}}{2 e ^{- 6 t}} + c_{1} e^{6 t}

\frac{d}{d x} (x^{4} - 3 x^{2} + 5 x + 2)

f (x) = arccot (x)

x \to \infty lim (- 3 + \frac{4}{x})

\frac{d}{d x} (sec (x))

y^{^{''}} - 4 y^{^{'}} + 8 y = - 28 cos (2 t) - 16 sin (2 t)

What is the solution for (dy)/(dt)=6y+te^{6t} ?
The solution for (dy)/(dt)=6y+te^{6t} is y=(t^2)/(2e^{-6t)}+c_{1}e^{6t}