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Popular >

x^{''}+8x^'+16=0

Solution

x^{^{''}} + 8 x^{^{'}} + 16 = 0

Solution

x = c_{1} + c_{2} e^{- 8 t} - 2 t

Solution steps

x^{''} (t) + 8 x^{'} (t) + 16 = 0

Solve linear ODE:

x = c_{1} + c_{2} e^{- 8 t} - 2 t

x = c_{1} + c_{2} e^{- 8 t} - 2 t

Graph

Popular Examples

y^{''}+5y^'+6y=e^{-t}

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{- t}

x^{''''}-x^{''}=1

x^{^{''''}} - x^{^{''}} = 1

y^{''}-2y^'+y=3e^t,y(0)=1,y^'(0)=1

y^{^{''}} - 2 y^{^{'}} + y = 3 e^{t}, y (0) = 1, y^{^{'}} (0) = 1

y^{''}-4y^'-5y=125

y^{^{''}} - 4 y^{^{'}} - 5 y = 125

y^{''}+4y^'+5y=-5x+3e^{-x}

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 3 e^{- x}

Frequently Asked Questions (FAQ)

What is the solution for x^{''}+8x^'+16=0 ?
The solution for x^{''}+8x^'+16=0 is x=c_{1}+c_{2}e^{-8t}-2t