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Popular >

x^{''}+4x^'+4=0

Solution

x^{^{''}} + 4 x^{^{'}} + 4 = 0

Solution

x = c_{1} + c_{2} e^{- 4 t} - t

Solution steps

x^{''} (t) + 4 x^{'} (t) + 4 = 0

Solve linear ODE:

x = c_{1} + c_{2} e^{- 4 t} - t

x = c_{1} + c_{2} e^{- 4 t} - t

Graph

Popular Examples

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

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{( 1 + t ^{2} ) + 3 e ^{t}}

y^{''}+2y^'+y=2cos(x)

y^{^{''}} + 2 y^{^{'}} + y = 2 cos (x)

y^{''}+2y^'+2y=4cos(t)+2sin(t)

y^{^{''}} + 2 y^{^{'}} + 2 y = 4 cos (t) + 2 sin (t)

y^{''}+10y^'+25y=100sinh(5x)

y^{^{''}} + 10 y^{^{'}} + 25 y = 100 sinh (5 x)

y^{''}+2y^'+y=9e^{-t}

y^{^{''}} + 2 y^{^{'}} + y = 9 e^{- t}

Frequently Asked Questions (FAQ)

What is the solution for x^{''}+4x^'+4=0 ?
The solution for x^{''}+4x^'+4=0 is x=c_{1}+c_{2}e^{-4t}-t