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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int cos (n) x d x

y = 2 x^{3} - x^{2} + \frac{4}{x}, (4, 1)

x y^{^{''}} + y^{^{'}} = 4 x

y^{^{'}} = 2 (1 + y^{2})

x \to 0 - lim (\frac{5}{2 x})

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