What is the solution for 2y^{''}-9y^'-18y=0,y(0)=8,y^'(0)=7 ?

The solution for 2y^{''}-9y^'-18y=0,y(0)=8,y^'(0)=7 is y=(8-82/15)e^{6t}+82/15 e^{-(3t)/2}

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2y^{''}-9y^'-18y=0,y(0)=8,y^'(0)=7

2 y^{^{''}} - 9 y^{^{'}} - 18 y = 0, y (0) = 8, y^{^{'}} (0) = 7

y = (8 - \frac{82}{15}) e^{6 t} + \frac{82}{15} e^{- \frac{3 t}{2}}

Solution steps

2 y^{''} (t) - 9 y^{'} (t) - 18 y = 0

Solve linear ODE:

y = (8 - \frac{82}{15}) e^{6 t} + \frac{82}{15} e^{- \frac{3 t}{2}}

y = (8 - \frac{82}{15}) e^{6 t} + \frac{82}{15} e^{- \frac{3 t}{2}}

\frac{d}{d x} (\frac{1 + csc ( x ^{9} )}{1 - cot ( x ^{9} )})

\int \frac{5}{x 4 - 25 ln ^{2} ( x )} d x

x (x^{4} - 1)^{6}

\int \frac{2 ln ( x )}{x} d x

\frac{\partial}{\partial y} (ln (2 w^{3} - 7 y + 3 x y^{2}))

What is the solution for 2y^{''}-9y^'-18y=0,y(0)=8,y^'(0)=7 ?
The solution for 2y^{''}-9y^'-18y=0,y(0)=8,y^'(0)=7 is y=(8-82/15)e^{6t}+82/15 e^{-(3t)/2}