What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)-15y=0 ?

The solution for (d^2y)/(dx^2)-2(dy)/(dx)-15y=0 is y=c_{1}e^{5x}+c_{2}e^{-3x}

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(d^2y)/(dx^2)-2(dy)/(dx)-15y=0

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 15 y = 0

y = c_{1} e^{5 x} + c_{2} e^{- 3 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 15 y = 0

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 3 x}

y = c_{1} e^{5 x} + c_{2} e^{- 3 x}

y^{^{''}} - 19 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = 1

x^{^{'''}} - 2 x^{^{''}} - x^{^{'}} + 2 x = 0

y^{^{''}} + 40 y^{^{'}} + 4000 y = 0

y^{^{''}} + 20 y^{^{'}} + 64 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} + 3 y = 0, y (0) = 6, y^{^{'}} (0) = - 2

What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)-15y=0 ?
The solution for (d^2y)/(dx^2)-2(dy)/(dx)-15y=0 is y=c_{1}e^{5x}+c_{2}e^{-3x}