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Popular >

y^{''}+2y^'-8y=4e^{-2x}-e^{-x}

Solution

y^{^{''}} + 2 y^{^{'}} - 8 y = 4 e^{- 2 x} - e^{- x}

Solution

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} - \frac{1}{2} e^{- 2 x} + \frac{1}{9} e^{- x}

Solution steps

y^{''} (x) + 2 y^{'} (x) - 8 y = 4 e^{- 2 x} - e^{- x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} - \frac{1}{2} e^{- 2 x} + \frac{1}{9} e^{- x}

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} - \frac{1}{2} e^{- 2 x} + \frac{1}{9} e^{- x}

Graph

Popular Examples

y^{''}-4y^'+4y=(x+1)*e^{2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = (x + 1) \cdot e^{2 x}

y^{''}+6y^'+13y=10e^{-2t},y(0)=3

y^{^{''}} + 6 y^{^{'}} + 13 y = 10 e^{- 2 t}, y (0) = 3

4y^{''}+y=sin(t),y(0)=0,y^'(0)=1

4 y^{^{''}} + y = sin (t), y (0) = 0, y^{^{'}} (0) = 1

y^{''}+16y=cos(4x)+sin(4x),y^0=3,y^'0=5

y^{^{''}} + 16 y = cos (4 x) + sin (4 x), y^{0} = 3, y^{^{'}} 0 = 5

y^{'''}+289y^'=tan(17x)

y^{^{'''}} + 289 y^{^{'}} = tan (17 x)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+2y^'-8y=4e^{-2x}-e^{-x} ?
The solution for y^{''}+2y^'-8y=4e^{-2x}-e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-4x}-1/2 e^{-2x}+1/9 e^{-x}