What is the solution for (d^2y)/(dt^2)+5(dy)/(dt)+6y=1 ?

The solution for (d^2y)/(dt^2)+5(dy)/(dt)+6y=1 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+1/6

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(d^2y)/(dt^2)+5(dy)/(dt)+6y=1

\frac{d ^{2} y}{d t ^{2}} + 5 \frac{d y}{d t} + 6 y = 1

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{1}{6}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 5 \frac{d y}{d t} + 6 y = 1

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{1}{6}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{1}{6}

x y^{2} y^{^{'}} = y^{3} - 4 x^{3}, y (1) = 4

\frac{( - \frac{1}{4} )}{1 + ( \frac{1}{2} ) \cdot s}

\frac{d}{d x} ((arctan (x))^{2})

x \to 1 + lim (\frac{1}{x + 8})

\frac{\partial}{\partial x} (- 6 y sin (3 x))

What is the solution for (d^2y)/(dt^2)+5(dy)/(dt)+6y=1 ?
The solution for (d^2y)/(dt^2)+5(dy)/(dt)+6y=1 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+1/6