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Popular >

y^{'''}-4y^{''}-y^'+4y=e^{6x}

Solution

y^{^{'''}} - 4 y^{^{''}} - y^{^{'}} + 4 y = e^{6 x}

Solution

y = c_{1} e^{4 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{70} e^{6 x}

Solution steps

y^{'''} (x) - 4 y^{''} (x) - y^{'} (x) + 4 y = e^{6 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{70} e^{6 x}

y = c_{1} e^{4 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{70} e^{6 x}

Graph

Popular Examples

y^{''}+36y=2cos(6x)+3sin(6x)

y^{^{''}} + 36 y = 2 cos (6 x) + 3 sin (6 x)

y^{''}-3y^'=te^{3t},y(0)=0,y^'(0)=2

y^{^{''}} - 3 y^{^{'}} = t e^{3 t}, y (0) = 0, y^{^{'}} (0) = 2

y^{''}-12y^'+35y=-40e^-3t

y^{^{''}} - 12 y^{^{'}} + 35 y = - 40 e^{-} 3 t

y^{''}+2y^'+5y=g(t),y(0)=-4,y^'(0)=0

y^{^{''}} + 2 y^{^{'}} + 5 y = g (t), y (0) = - 4, y^{^{'}} (0) = 0

y^{''}-4y^'+5y=12e^t,y(0)=6,y^'(0)=7

y^{^{''}} - 4 y^{^{'}} + 5 y = 12 e^{t}, y (0) = 6, y^{^{'}} (0) = 7

Frequently Asked Questions (FAQ)

What is the solution for y^{'''}-4y^{''}-y^'+4y=e^{6x} ?
The solution for y^{'''}-4y^{''}-y^'+4y=e^{6x} is y=c_{1}e^{4x}+c_{2}e^{-x}+c_{3}e^x+1/70 e^{6x}