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Popular >

y^{'''}-2y^{''}-5y^'+6y=2e^x(1-6x)

Solution

y^{^{'''}} - 2 y^{^{''}} - 5 y^{^{'}} + 6 y = 2 e^{x} (1 - 6 x)

Solution

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

Solution steps

y^{'''} (x) - 2 y^{''} (x) - 5 y^{'} (x) + 6 y = 2 e^{x} (1 - 6 x)

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''}-y^'-2y=3e^{2x}-4e^{3x}

y^{^{''}} - y^{^{'}} - 2 y = 3 e^{2 x} - 4 e^{3 x}

x^{''}+3x^'+33x=11cos(5t)

x^{^{''}} + 3 x^{^{'}} + 33 x = 11 cos (5 t)

y^{''}+10y^'+16y=12cos(2x)+4sin(2x)

y^{^{''}} + 10 y^{^{'}} + 16 y = 12 cos (2 x) + 4 sin (2 x)

y^{'''}-y^{''}-12y^'=x-2xe^{-3x}

y^{^{'''}} - y^{^{''}} - 12 y^{^{'}} = x - 2 x e^{- 3 x}

y^{''}+y=u_{3}(t),y(0)=0,y^'(0)=1

y^{^{''}} + y = u_{3} (t), y (0) = 0, y^{^{'}} (0) = 1

Frequently Asked Questions (FAQ)

What is the solution for y^{'''}-2y^{''}-5y^'+6y=2e^x(1-6x) ?
The solution for y^{'''}-2y^{''}-5y^'+6y=2e^x(1-6x) is y=c_{1}e^x+c_{2}e^{-2x}+c_{3}e^{3x}+e^xx^2