What is the solution for y^{''}+6y^'=162e^{3t},y(0)=6,y^'(0)=7 ?

The solution for y^{''}+6y^'=162e^{3t},y(0)=6,y^'(0)=7 is y=-11/6+11/6 e^{-6t}+6e^{3t}

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y^{''}+6y^'=162e^{3t},y(0)=6,y^'(0)=7

y^{^{''}} + 6 y^{^{'}} = 162 e^{3 t}, y (0) = 6, y^{^{'}} (0) = 7

y = - \frac{11}{6} + \frac{11}{6} e^{- 6 t} + 6 e^{3 t}

Solution steps

y^{''} (t) + 6 y^{'} (t) = 162 e^{3 t}

Solve linear ODE:

y = - \frac{11}{6} + \frac{11}{6} e^{- 6 t} + 6 e^{3 t}

y = - \frac{11}{6} + \frac{11}{6} e^{- 6 t} + 6 e^{3 t}

t \to \infty lim (\frac{0.2 t}{t ^{2} + 1})

\frac{d}{d x} (2 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}}))

x \to 5 lim (2 x^{3} - 3 x^{2} - x - 4)

t y^{^{'}} + y = t

f (x) = \frac{6 x ^{5}}{5} - x + 3 e^{x}

What is the solution for y^{''}+6y^'=162e^{3t},y(0)=6,y^'(0)=7 ?
The solution for y^{''}+6y^'=162e^{3t},y(0)=6,y^'(0)=7 is y=-11/6+11/6 e^{-6t}+6e^{3t}