What is the solution for y^{''}-y=0,y(0)=6 ?

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

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y^{''}-y=0,y(0)=6

y^{^{''}} - y = 0, y (0) = 6

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

Solution steps

y^{''} (t) - y = 0

Solve linear ODE:

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

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

\int \frac{x}{( 1 + x ^{2} )} d x

x \to - 1 lim (\frac{x ^{3} + 1}{x - 1})

\int \frac{x ^{2}}{( x ^{2} + 1 )} d x

1 - 1 e^{(- t - 2)}

2 x - x^{2}, x^{2}

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