What is the solution for (d^3y)/(dx^3)+3(d^2y)/(dx^2)-4y=0 ?

The solution for (d^3y)/(dx^3)+3(d^2y)/(dx^2)-4y=0 is y=c_{1}e^x+c_{2}e^{-2x}+c_{3}xe^{-2x}

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(d^3y)/(dx^3)+3(d^2y)/(dx^2)-4y=0

\frac{d ^{3} y}{d x ^{3}} + 3 \frac{d ^{2} y}{d x ^{2}} - 4 y = 0

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} x e^{- 2 x}

Solution steps

\frac{d ^{3} y}{d x ^{3}} + 3 \frac{d ^{2} y}{d x ^{2}} - 4 y = 0

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} x e^{- 2 x}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} x e^{- 2 x}

y^{^{''}} + k y^{^{'}} + 8 y = 0

100 y^{^{''}} - 140 y^{^{'}} + 85 y = 0, y (2) = 9, y^{^{'}} (2) = 8

x^{^{''}} - 6 x = 0

y^{^{''}} + y^{^{'}} - \frac{10}{3} y = 0

x^{^{''}} + 8 x^{^{'}} + 4 x = 0

What is the solution for (d^3y)/(dx^3)+3(d^2y)/(dx^2)-4y=0 ?
The solution for (d^3y)/(dx^3)+3(d^2y)/(dx^2)-4y=0 is y=c_{1}e^x+c_{2}e^{-2x}+c_{3}xe^{-2x}