What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)-63y=0 ?

The solution for (d^2y)/(dx^2)+2(dy)/(dx)-63y=0 is y=c_{1}e^{7x}+c_{2}e^{-9x}

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(d^2y)/(dx^2)+2(dy)/(dx)-63y=0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 63 y = 0

y = c_{1} e^{7 x} + c_{2} e^{- 9 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 63 y = 0

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} e^{- 9 x}

y = c_{1} e^{7 x} + c_{2} e^{- 9 x}

25 y^{^{''}} + 80 y^{^{'}} + 64 y = 0, y (0) = 8

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 9, y^{^{'}} (0) = 5

7 y^{^{''}} - 8 y^{^{'}} + y = 0, y (0) = 7, y^{^{'}} (0) = \frac{1}{7}

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = \frac{3}{5}, y^{^{'}} (0) = \frac{1}{5}

y^{^{''}} + 16 y = 0, y (0) = sin (k t)

What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)-63y=0 ?
The solution for (d^2y)/(dx^2)+2(dy)/(dx)-63y=0 is y=c_{1}e^{7x}+c_{2}e^{-9x}