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

The solution for (d^2y)/(dx^2)-10(dy)/(dx)-3y=0 is y=c_{1}e^{(5+2sqrt(7))x}+c_{2}e^{(5-2sqrt(7))x}

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

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

y = c_{1} e^{(5 + 27) x} + c_{2} e^{(5 - 27) x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{(5 + 27) x} + c_{2} e^{(5 - 27) x}

y = c_{1} e^{(5 + 27) x} + c_{2} e^{(5 - 27) x}

y^{^{''}} + 15 y = 0, y (0) = sin (k t)

y^{^{''}} - \frac{1}{c} y = 0

2 y^{^{''}} + 12 y = 0

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

y^{^{''}} - 3 y^{^{'}} + 5 y = 0

What is the solution for (d^2y)/(dx^2)-10(dy)/(dx)-3y=0 ?
The solution for (d^2y)/(dx^2)-10(dy)/(dx)-3y=0 is y=c_{1}e^{(5+2sqrt(7))x}+c_{2}e^{(5-2sqrt(7))x}