What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+10y=0 ?

The solution for (d^2y)/(dx^2)-6(dy)/(dx)+10y=0 is y=e^{3x}(c_{1}cos(x)+c_{2}sin(x))

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(d^2y)/(dx^2)-6(dy)/(dx)+10y=0

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 10 y = 0

y = e^{3 x} (c_{1} cos (x) + c_{2} sin (x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 10 y = 0

Solve linear ODE:

y = e^{3 x} (c_{1} cos (x) + c_{2} sin (x))

y = e^{3 x} (c_{1} cos (x) + c_{2} sin (x))

y^{^{''}} + 8 y^{^{'}} - 2 y = 0

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

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 3 y = 0

\frac{d ^{4} y}{d x ^{4}} + 6 \frac{d ^{2} y}{d x ^{2}} + 8 y = 0

y^{^{''}} + 9 y^{^{'}} - 20 y = 0

What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+10y=0 ?
The solution for (d^2y)/(dx^2)-6(dy)/(dx)+10y=0 is y=e^{3x}(c_{1}cos(x)+c_{2}sin(x))