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

The solution for y^{''}-9y=0,y(0)=7 is y=(7-c_{2})e^{3t}+c_{2}e^{-3t}

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

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

y = (7 - c_{2}) e^{3 t} + c_{2} e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = (7 - c_{2}) e^{3 t} + c_{2} e^{- 3 t}

y = (7 - c_{2}) e^{3 t} + c_{2} e^{- 3 t}

\int \frac{3}{( x + 3 ) ^{2}} d x

f (x) = 3^{x^{2} - x + 5}

\frac{d y}{d x} + 7 = e^{7 x + y - 5}

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

\int cos (x) e^{- 3 x} d x

What is the solution for y^{''}-9y=0,y(0)=7 ?
The solution for y^{''}-9y=0,y(0)=7 is y=(7-c_{2})e^{3t}+c_{2}e^{-3t}