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^{3x}+c_{2}e^{-5x}

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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^{3 x} + c_{2} e^{- 5 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^{3 x} + c_{2} e^{- 5 x}

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

77 y^{^{''''}} + 338 y^{^{''}} + 225 y = 0

y^{^{''}} = 10 y

\frac{d ^{2} y}{d x ^{2}} = a^{2} y

y^{^{'''}} + y^{^{''}} + y^{^{'}} - 3 y = 0

y^{^{''}} + 25 y = 0, y (0) = 4, y^{^{'}} (0) = - 5

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^{3x}+c_{2}e^{-5x}