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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + \frac{16}{3} y = 0

4 y^{^{''}} + 22 y^{^{'}} + 18 y = 0, y (0) = 3, y^{^{'}} (0) = 0

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

y^{^{''}} + 10.5 y = 0

\frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} - 12 y = 0

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