What is the solution for (d^2y)/(dx^2)(1)+(dy)/(dx)(10)+9y=18 ?

The solution for (d^2y)/(dx^2)(1)+(dy)/(dx)(10)+9y=18 is y=c_{1}e^{-x}+c_{2}e^{-9x}+2

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(d^2y)/(dx^2)(1)+(dy)/(dx)(10)+9y=18

\frac{d ^{2} y}{d x ^{2}} (1) + \frac{d y}{d x} (10) + 9 y = 18

y = c_{1} e^{- x} + c_{2} e^{- 9 x} + 2

Solution steps

\frac{d ^{2} y}{d x ^{2}} (1) + \frac{d y}{d x} (10) + 9 y = 18

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 9 x} + 2

y = c_{1} e^{- x} + c_{2} e^{- 9 x} + 2

y^{^{''}} + 2 y^{^{'}} + 4 y = t cos (t)

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 sin (x)

y^{^{''}} - 2 y^{^{'}} + y = e^{3 x} + e^{2 x}

(D^{2} - 4 D + 4) y = sin (3 x)

y^{^{''}} - 2 y^{^{'}} - 15 = 0, y (0) = 2, y^{^{'}} (0) = 6

What is the solution for (d^2y)/(dx^2)(1)+(dy)/(dx)(10)+9y=18 ?
The solution for (d^2y)/(dx^2)(1)+(dy)/(dx)(10)+9y=18 is y=c_{1}e^{-x}+c_{2}e^{-9x}+2