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Popular >

y^{'''}+6y=0

Solution

y^{^{'''}} + 6 y = 0

Solution

y = c_{1} e^{- 36 t} + e^{3 \frac{3}{4} t} (c_{2} cos (\frac{6 243 t}{4 ^{\frac{1}{3}}}) + c_{3} sin (\frac{6 243 t}{4 ^{\frac{1}{3}}}))

Solution steps

y^{'''} (t) + 6 y = 0

Solve linear ODE:

y = c_{1} e^{- 36 t} + e^{3 \frac{3}{4} t} (c_{2} cos (\frac{6 243 t}{4 ^{\frac{1}{3}}}) + c_{3} sin (\frac{6 243 t}{4 ^{\frac{1}{3}}}))

y = c_{1} e^{- 36 t} + e^{3 \frac{3}{4} t} (c_{2} cos (\frac{6 243 t}{4 ^{\frac{1}{3}}}) + c_{3} sin (\frac{6 243 t}{4 ^{\frac{1}{3}}}))

Graph

Popular Examples

1/2 y^{''}+20y=0

\frac{1}{2} y^{^{''}} + 20 y = 0

y^{''}+0y^'+36y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 0 y^{^{'}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 0

- 3 y^{^{''}} + 12 y = 0

y^{''}+120y^'+10000y=0

y^{^{''}} + 120 y^{^{'}} + 10000 y = 0

y^{'''}-18y^{''}+108y^'-216y=0

y^{^{'''}} - 18 y^{^{''}} + 108 y^{^{'}} - 216 y = 0

Frequently Asked Questions (FAQ)

What is the solution for y^{'''}+6y=0 ?
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