What is the solution for (d^2y)/(dx^2)+3(dy)/(dx)-10y=0 ?

The solution for (d^2y)/(dx^2)+3(dy)/(dx)-10y=0 is y=c_{1}e^{2x}+c_{2}e^{-5x}

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(d^2y)/(dx^2)+3(dy)/(dx)-10y=0

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 10 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 10 y = 0

Solve linear ODE:

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

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

x^{^{''}} = 2 x

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''''}} + 20 y^{^{''}} + 64 y = 0

y^{^{''''}} - 9 y^{^{''}} = 0

What is the solution for (d^2y)/(dx^2)+3(dy)/(dx)-10y=0 ?
The solution for (d^2y)/(dx^2)+3(dy)/(dx)-10y=0 is y=c_{1}e^{2x}+c_{2}e^{-5x}