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Popular >

(d^6-1)y=0

Solution

(d^{6} - 1) y = 0

Solution

y = c_{1} e^{x} + c_{2} e^{- x} + e^{\frac{x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + e^{- \frac{x}{2}} (c_{5} cos (\frac{3 x}{2}) + c_{6} sin (\frac{3 x}{2}))

Solution steps

(d^{6} - 1) y = 0

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + e^{\frac{x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + e^{- \frac{x}{2}} (c_{5} cos (\frac{3 x}{2}) + c_{6} sin (\frac{3 x}{2}))

y = c_{1} e^{x} + c_{2} e^{- x} + e^{\frac{x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + e^{- \frac{x}{2}} (c_{5} cos (\frac{3 x}{2}) + c_{6} sin (\frac{3 x}{2}))

Graph

Popular Examples

1/2 y^{''}+2y^'+6y=0

\frac{1}{2} y^{^{''}} + 2 y^{^{'}} + 6 y = 0

y^{''}+16y=0,y(0)=0,y(1)=1

y^{^{''}} + 16 y = 0, y (0) = 0, y (1) = 1

(d^2)/(dt^2)(θ(t))+gθ(t)=0

\frac{d ^{2}}{d t ^{2}} (θ (t)) + g θ (t) = 0

15y^{''}+90y^'+135y=0,y(0)=3,y^'(0)=0

15 y^{^{''}} + 90 y^{^{'}} + 135 y = 0, y (0) = 3, y^{^{'}} (0) = 0

12y^{''}+64y=0,y(0)=4,y^'(0)=7

12 y^{^{''}} + 64 y = 0, y (0) = 4, y^{^{'}} (0) = 7

Frequently Asked Questions (FAQ)

What is the solution for (d^6-1)y=0 ?
The solution for (d^6-1)y=0 is